{"id":28165,"date":"2021-08-16T19:12:16","date_gmt":"2021-08-16T11:12:16","guid":{"rendered":"https:\/\/swarma.org\/?p=28165"},"modified":"2021-08-16T19:12:16","modified_gmt":"2021-08-16T11:12:16","slug":"%e6%b7%b7%e6%b2%8c%e6%95%b0%e5%ad%a6%e7%90%86%e8%ae%ba%e4%bb%8e%e5%a5%b9%e7%ac%94%e4%b8%8b%e6%82%84%e6%82%84%e6%b5%81%e5%87%ba%e4%b8%a8%e9%99%88%e5%85%b3%e8%8d%a3","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=28165","title":{"rendered":"\u6df7\u6c8c\u6570\u5b66\u7406\u8bba\u4ece\u5979\u7b14\u4e0b\u6084\u6084\u6d41\u51fa\u4e28\u9648\u5173\u8363"},"content":{"rendered":"
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\u5199\u6df7\u6c8c<\/span>\uff08Chaos\uff09<\/span>\u6570\u5b66\u7406\u8bba\u7684\u53d1\u5c55\u53f2\uff0c\u5982\u679c\u4e0d\u63d0\u53ca Mary Cartwright\u7684\u8bdd\u65e0\u8bba\u5982\u4f55\u662f\u4e0d\u5b8c\u6574\u7684\uff0c\u4e5f\u662f\u4e0d\u516c\u5141\u7684\u3002<\/span><\/p>\n


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\u5973\u7235\u58eb\u739b\u4e3d \u00b7\u9732\u897f \u00b7\u5361\u7279\u8d56\u7279<\/span>\uff08Dame Mary Lucy Cartwright\uff0c1900\u5e7412\u670817 \u65e5\u2014 1998\u5e744\u67083\u65e5\uff09<\/span>\u662f\u4e3a\u6570\u4e0d\u591a\u7684\u957f\u5bff\u6570\u5b66\u5bb6\u4e4b\u4e00\u3002<\/span>
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\u56fe1  \u739b\u4e3d \u00b7\u5361\u7279\u8d56\u7279\uff081900-1998\uff09<\/span><\/p>\n


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\u739b\u4e3d\u00b7\u5361\u7279\u8d56\u7279\u51fa\u751f\u4e8e\u82f1\u683c\u5170\u897f\u90e8\u5317\u5b89\u666e\u6566\u90e1 Aynho\u6751\u7684\u4e00\u4e2a\u4ece\u4e8b\u516c\u76ca\u4e8b\u4e1a\u7684\u4f20\u7edf\u5bb6\u5ead\u91cc\u3002\u7236\u4eb2William D. Cartwright\u66fe\u662fAynho\u5c0f\u5b66\u6821\u957f\uff0c\u6bcd\u4eb2\u540d\u53ebLucy H. M. Bury\uff0c\u739b\u4e3d\u5728\u5bb6\u6392\u884c\u7b2c\u4e09\uff0c\u4e24\u4e2a\u54e5\u54e5\u6b7b\u4e8e\u7b2c\u4e00\u6b21\u4e16\u754c\u5927\u6218\u6218\u4e71\u4e4b\u4e2d\uff0c\u7559\u4e0b\u5979\u548c\u59b9\u59b9 Jane\u4ee5\u53ca\u5c0f\u5f1f\u5f1f William\u3002<\/span><\/p>\n


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1917\u5e74\uff0c\u6216\u8bb8\u662f\u7531\u4e8e\u5979\u8868\u59d0Cecily Ady\u5728\u725b\u6d25\u5927\u5b66St. Hugh College\u6559\u5386\u53f2\u7684\u7f18\u6545\uff0c\u739b\u4e3d\u8003\u8fdb\u4e86\u8be5\u5b66\u9662\u3002\u4f46\u662f\uff0c\u5728\u90a3\u91cc\u5979\u5374\u6ca1\u6709\u4fee\u8bfb\u81ea\u5df1\u672c\u6765\u559c\u6b22\u7684\u5386\u53f2\u4e13\u4e1a\uff0c\u539f\u56e0\u662f\u5acc\u5386\u53f2\u8bfe\u7a0b\u4f5c\u4e1a\u592a\u591a\uff0c\u800c\u53bb\u5b66\u4e60\u6570\u5b66\u3002\u5f53\u5e74\uff0c\u8fde\u5979\u5728\u5185\u6574\u4e2a\u725b\u6d25\u5927\u5b66\u53ea\u67095\u540d\u5973\u751f\u8bfb\u6570\u5b66\u3002\u5979\u88ab\u8457\u540d\u6570\u5b66\u5bb6\u6208\u5f17\u96f7\u00b7\u54c8\u4ee3<\/span>\uff08Godfrey H. Hardy\uff0c1877-1947\uff09<\/span>\u7834\u4f8b\u63a5\u7eb3\u5230\u4ed6\u4e00\u5411\u53ea\u6709\u7537\u751f\u7684\u6570\u5b66\u8bfe\u7a0b\u3002\u5728\u90a3\u91cc\uff0c\u739b\u4e3d\u88ab\u8270\u96be\u5374\u4f18\u96c5\u7684\u6570\u5b66\u7406\u8bba\u6df1\u6df1\u5438\u5f15\u30021923\u5e74\uff0c\u5979\u4ece\u725b\u6d25\u5927\u5b66\u6bd5\u4e1a\uff0c\u662f\u82f1\u56fd\u7b2c\u4e00\u4e2a\u83b7\u5f97\u201c\u6570\u5b66\u4e00\u7b49\u4f18\u79c0\u751f\u201d<\/span>\uff08first class degree in mathematics\uff09<\/span>\u8363\u8a89\u7684\u5973\u5927\u5b66\u751f\u3002\u968f\u540e\u7684\u56db\u5e74\u65f6\u95f4\u91cc\uff0c\u5979\u5148\u540e\u5728Alice Ottley School\u548c Wycombe Abbey School \u8bb2\u6388\u6570\u5b66\uff0c\u4f46\u5979\u7684\u5174\u8da3\u4ecd\u7136\u662f\u63a2\u7a76\u66f4\u6df1\u5965\u7684\u6570\u5b66\u3002<\/span><\/p>\n


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1928\u5e741\u6708\uff0c\u739b\u4e3d\u79bb\u5f00\u4e86\u6559\u5b66\u804c\u4f4d\uff0c\u56de\u5230\u725b\u6d25\u52a0\u5165\u54c8\u4ee3\u7684\u6570\u5b66\u7814\u7a76\u5c0f\u7ec4\u7ee7\u7eed\u6df1\u9020\u3002\u5f53\u5e74\u54c8\u4ee3\u7ed9\u5b66\u751f\u6388\u8bfe\u7684\u65b9\u5f0f\u6709\u70b9\u7279\u522b\uff1a\u4ed6\u901a\u5e38\u662f\u5148\u8bb2\u4e00\u4e2a\u5c0f\u65f6\u7684\u8bfe\uff0c\u7136\u540e\u8ba9\u5927\u5bb6\u805a\u5728\u4e00\u8d77\u559d\u8336\u5403\u70b9\u5fc3\uff0c\u7ee7\u7eed\u8ba8\u8bba\u8bfe\u7a0b\u4e2d\u7684\u6570\u5b66\u95ee\u9898\uff0c\u5076\u5c14\u4e5f\u95f2\u804a\u4e00\u4e9b\u6570\u5b66\u5bb6\u8f76\u4e8b\u3002\u5728\u90a3\u91cc\uff0c\u739b\u4e3d\u671f\u672b\u8003\u8bd5\u540d\u5217\u7b2c\u4e00\u3002\u7279\u522b\u662f\uff0c\u5979\u5728\u542c\u5b8c\u54c8\u4ee3\u51e0\u4e2a\u5173\u4e8eDirichlet\u7ea7\u6570\u7684Abel\u6c42\u548c\u8bb2\u5ea7\u4e4b\u540e\uff0c\u51fa\u8272\u5730\u7528\u56f4\u9053\u79ef\u5206\u65b9\u6cd5\u5b8c\u5168\u89e3\u51b3\u4e86\u54c8\u4ee3\u7559\u4e0b\u7684\u4e00\u4e2a\u91cd\u8981\u800c\u53c8\u56f0\u96be\u7684\u95ee\u9898\uff0c\u8ba9\u54c8\u4ee3\u9887\u4e3a\u60ca\u8bb6\u3002\u591a\u5e74\u4e4b\u540e\uff0c\u54c8\u4ee3\u5728\u5176\u540d\u8457\u300a\u53d1\u6563\u7ea7\u6570\u300b<\/span>\uff08Divergent Series<\/em>\uff0c1948\uff09<\/span>\u4e2d\u6536\u5f55\u4e86\u739b\u4e3d\u7684\u79ef\u5206\u65b9\u6cd5\u53ca\u5176\u5728Fourier\u7ea7\u6570\u4e2d\u7684\u5e94\u7528\u3002<\/span><\/p>\n


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1928-1929\u5e74\u95f4\uff0c\u54c8\u4ee3\u5230\u7f8e\u56fd\u666e\u6797\u65af\u987f\u5927\u5b66\u4f5c\u5b66\u672f\u8bbf\u95ee\uff0c\u4e34\u8d70\u65f6\u628a\u739b\u4e3d\u63a8\u8350\u7ed9\u7ee7\u627f\u81ea\u5df1Savilian \u8bb2\u5ea7\u6559\u6388\u4f4d\u7f6e\u7684\u7231\u5fb7\u534e\u00b7\u8482\u5947\u9a6c\u4ec0<\/span>\uff08Edward C. Titchmarsh\uff0c1899-1963\uff09<\/span>\u3002\u8482\u5947\u9a6c\u4ec0\u628a\u739b\u4e3d\u7684\u7814\u7a76\u5174\u8da3\u5e26\u8fdb\u4e86\u590d\u53d8\u51fd\u6570\u5206\u6790\u9886\u57df\uff0c\u5e76\u914d\u5408\u54c8\u4ee3\u6307\u5bfc\u5979\u7684\u535a\u58eb\u8bba\u6587\u30021930\u5e74\uff0c\u739b\u4e3d\u4f5c\u4e3a\u725b\u6d25\u5927\u5b66\u5386\u53f2\u4e0a\u7b2c\u4e00\u4e2a\u5973\u6570\u5b66\u535a\u58eb\u6bd5\u4e1a\uff0c\u8bba\u6587\u9898\u76ee\u662f\u201c\u7279\u6b8a\u7c7b\u578b\u79ef\u5206\u51fd\u6570\u7684\u96f6\u70b9\u201d<\/span>\uff08\u201cThe Zeros of Integral Functions of Special Types\u201d\uff09<\/span>\u3002\u5728\u535a\u58eb\u5b66\u4f4d\u7b54\u8fa9\u59d4\u5458\u4f1a\u91cc\uff0c\u4e00\u4f4d\u91cd\u8981\u7684\u6210\u5458\u662f\u54c8\u4ee3\u7684\u957f\u671f\u5408\u4f5c\u8005\u3001\u5251\u6865\u5927\u5b66Trinity College\u7684\u6570\u5b66\u6559\u6388\u7ea6\u7ff0\u00b7\u674e\u7279\u5c14\u4f0d\u5fb7<\/span>\uff08John E. Littlewood\uff0c1885-1977\uff09<\/span>\u3002\u5f53\u5e74\uff0c\u54c8\u4ee3\u548c\u674e\u7279\u5c14\u4f0d\u5fb7\u4e24\u4eba\u5728\u82f1\u56fd\u7eaf\u7cb9\u6570\u5b66\u9886\u57df\u9996\u5c48\u4e00\u6307\uff0c\u5e76\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u6539\u53d8\u4e86\u6570\u5b66\u5206\u6790\u8fd9\u95e8\u5b66\u79d1\u7684\u53d1\u5c55\u65b9\u5411\u548c\u8fdb\u7a0b\u3002\u4ed6\u4fe9\u5408\u4f5c\u6210\u679c\u7d2f\u7d2f\uff0c\u5176\u4e2d\u6bd4\u8f83\u5e7f\u4e3a\u4eba\u77e5\u7684\u6709\u54c8\u4ee3\u2014\u674e\u7279\u5c14\u4f0d\u5fb7\u5b9a\u7406\u3001\u54c8\u4ee3\u2014\u674e\u7279\u5c14\u4f0d\u5fb7\u4e0d\u7b49\u5f0f\u3001\u54c8\u4ee3\u2014\u674e\u7279\u5c14\u4f0d\u5fb7\u6781\u5927\u51fd\u6570\u3001\u54c8\u4ee3\u2014\u674e\u7279\u5c14\u4f0d\u5fb7\u5706\u65b9\u6cd5\uff0c\u7b49\u7b49\u3002\u54c8\u4ee3\u7684\u5c0f\u518c\u5b50\u300a\u4e00\u4e2a\u6570\u5b66\u5bb6\u7684\u8fa9\u767d\u300b<\/span>\uff08A Mathematician\u2019s Apology<\/em>\uff0c1941\uff09<\/span>\u4e2d\u7684\u4e00\u53e5\u8bdd\u662f\u4f17\u6240\u5468\u77e5\u7684\uff1a\u201c\u771f\u6b63\u201d\u7684\u6570\u5b66\u51e0\u4e4e\u662f\u5b8c\u5168\u201c\u65e0\u7528\u201d\u7684\u3002\u674e\u7279\u5c14\u4f0d\u5fb7\u7684\u5c0f\u518c\u5b50\u300a\u6570\u5b66\u968f\u7b14\u96c6\u300b<\/span>\uff08A Mathematician\u2019s Miscellany<\/em>\uff0c1953\uff09<\/span>\u4e2d\u5173\u4e8e\u6700\u77ed\u7684\u6570\u5b66\u535a\u58eb\u8bba\u6587\u53ef\u4ee5\u53ea\u6709\u4e24\u53e5\u8bdd\u7684\u8bf4\u6cd5\u4e5f\u662f\u4f17\u6240\u5468\u77e5\u7684\uff1a\u4e00\u53e5\u91cd\u8981\u5b9a\u7406\u7684\u53d9\u8ff0\u52a0\u4e0a\u4e00\u53e5\u7b80\u6d01\u7684\u8bc1\u660e\u3002\u739b\u4e3d\u535a\u58eb\u6bd5\u4e1a\u540e\uff0c\u674e\u7279\u5c14\u4f0d\u5fb7\u548c\u5979\u4ea6\u5e08\u4ea6\u53cb\uff0c\u6210\u4e86\u957f\u671f\u6570\u5b66\u7814\u7a76\u5408\u4f5c\u4f19\u4f34\u3002<\/span><\/p>\n


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1930\u5e7410\u6708\uff0c\u739b\u4e3d\u83b7\u5f97\u4e86Yarrow \u57fa\u91d1\u7684\u8d44\u52a9\uff0c\u5230\u5251\u6865\u5927\u5b66\u683c\u987f\u5973\u5b50\u5b66\u9662<\/span>\uff08Girton College\uff09<\/span>\u7ee7\u7eed\u5979\u7684\u51fd\u6570\u7406\u8bba\u7814\u7a76\u3002\u5728\u90a3\u91cc\uff0c\u5979\u65c1\u542c\u4e86\u674e\u7279\u5c14\u4f0d\u5fb7\u7684\u51e0\u95e8\u51fd\u6570\u7406\u8bba\u8bfe\u7a0b\u5e76\u53c2\u52a0\u4ed6\u7ec4\u7ec7\u7684\u6570\u5b66\u8ba8\u8bba\u73ed\u3002\u671f\u95f4\uff0c\u739b\u4e3d\u5229\u7528\u62c9\u65af\u00b7\u963f\u5c14\u798f\u65af<\/span>\uff08Lars V. Ahlfors\uff0c1907-1996\uff09<\/span>\u7684\u4fdd\u5f62\u6620\u5c04\u7406\u8bba\u89e3\u51b3\u4e86\u674e\u7279\u5c14\u4f0d\u5fb7\u516c\u5f00\u7684\u4e00\u4e2a\u591a\u590d\u53d8\u51fd\u6570\u7684\u6781\u5927\u6a21\u7cbe\u786e\u4e0a\u754c\u4f30\u8ba1\u95ee\u9898\uff0c\u8ba9\u674e\u7279\u5c14\u4f0d\u5fb7\u5927\u4e3a\u8d5e\u8d4f\u3002\u90a3\u5c31\u662f\u8457\u540d\u7684\u201c\u5361\u7279\u8d56\u7279\u5b9a\u7406\u201d\uff0c1935\u5e74\u53d1\u8868\u5728Mathematische Annalen \u6742\u5fd7\uff0c\u5e76\u88ab\u674e\u7279\u5c14\u4f0d\u5fb7\u6536\u5f55\u8fdb\u4ed6\u7684\u6559\u79d1\u4e66\u300a\u51fd\u6570\u7406\u8bba\u8bb2\u4e49\u300b<\/span>\uff08Lectures on the Theory of Functions<\/em>\uff0c1944\uff09<\/span>\u3002\u8be5\u5b9a\u7406\u5728\u4eca\u5929\u4fe1\u53f7\u8fc7\u7a0b<\/span>\uff08Signal Processing\uff09<\/span>\u7684\u5e94\u7528\u7814\u7a76\u4e2d\u4f9d\u7136\u88ab\u7ecf\u5e38\u5f15\u7528\u3002<\/span><\/p>\n


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1931\u5e74\uff0c\u54c8\u4ee3\u4ece\u725b\u6d25\u5230\u5251\u6865\u63a5\u53d7\u4e86Sadleirian\u8bb2\u5ea7\u6559\u6388\u804c\u4f4d\u30021935\u5e74\uff0c\u739b\u4e3d\u7559\u5728\u5251\u6865\u683c\u987f\u5b66\u9662\u62c5\u4efb\u52a9\u7406\u8bb2\u5e08\u3002<\/span><\/p>\n


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\u5f00\u59cb\uff0c\u739b\u4e3d\u4f9d\u7136\u6ce8\u91cd\u4e8e\u7eaf\u6570\u5b66\u7814\u7a76\u3002\u9664\u4e86\u4e0a\u9762\u63d0\u5230\u7684Dirichlet \u7ea7\u6570\u7684Abel\u6c42\u548c\u4ee5\u53ca\u591a\u590d\u53d8\u51fd\u6570\u7684\u6781\u5927\u6a21\u7406\u8bba\u4e4b\u5916\uff0c\u5979\u90a3\u4e2a\u65f6\u671f\u7684\u4e3b\u8981\u8d21\u732e\u5728\u51fd\u6570\u7406\u8bba\u3001\u79ef\u5206\u51fd\u6570\u7684\u96f6\u70b9\u3001\u89e3\u6790\u51fd\u6570\u5728\u5355\u4f4d\u5706\u4e0a\u7684\u6b63\u5219\u6027\u3001Borel \u6269\u6563\u7b49\u65b9\u9762\u3002<\/span><\/p>\n


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\u540e\u6765\uff0c\u739b\u4e3d\u6700\u5e7f\u4e3a\u4eba\u77e5\u7684\u5e94\u7528\u6570\u5b66\u6210\u679c\u662f\u548c\u674e\u7279\u5c14\u4f0d\u5fb7\u5408\u4f5c\u7684\u5173\u4e8e\u8377\u5170\u7269\u7406\u5b66\u5bb6\u8303\u5fb7\u6ce2\u5c14<\/span>\uff08Balthasar van del Pol\uff0c1889-1959\uff09<\/span>\u5fae\u5206\u65b9\u7a0b\u7684\u7814\u7a76\uff0c\u5c24\u5176\u662f\u5979\u5173\u4e8e\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u89e3\u7684\u5b58\u5728\u6027\u548c\u632f\u8361\u884c\u4e3a\u7684\u62d3\u6251\u5b66\u5206\u6790\u65b9\u6cd5\uff0c\u5f00\u542f\u4e86\u5bf9\u5177\u4f53\u6df7\u6c8c\u7269\u7406\u6a21\u578b\u7684\u6570\u5b66\u5206\u6790\u7814\u7a76\u5148\u6cb3\u3002<\/span><\/p>\n


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2. \u6df7\u6c8c\u6570\u5b66\u7406\u8bba\u7684\u66d9\u5149<\/strong><\/strong><\/p>\n<\/section>\n

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\u6545\u4e8b\u8fd8\u5f97\u4ece1938\u5e74\u8bf4\u8d77\u3002\u82f1\u56fd\u653f\u5e9c\u4e8e1916\u5e74\u5efa\u7acb\u7684\u79d1\u5b66\u4e0e\u5de5\u4e1a\u7814\u7a76\u603b\u7f72\u7edf\u8f96\u4e0b\u7684\u96f7\u8fbe\u7814\u7a76\u59d4\u5458\u4f1a\u7ed9\u4f26\u6566\u6570\u5b66\u4f1a\u53d1\u53bb\u4e86\u4e00\u9879\u7814\u7a76\u63d0\u6848\uff0c\u5e0c\u671b\u6570\u5b66\u5bb6\u4eec\u80fd\u591f\u5e2e\u5fd9\u89e3\u51b3\u96f7\u8fbe\u5de5\u7a0b\u7814\u7a76\u4e2d\u51fa\u73b0\u7684\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u7684\u6c42\u89e3\u548c\u5206\u6790\u95ee\u9898\uff0c\u4ee5\u671f\u201c\u66f4\u5168\u9762\u5730\u4e86\u89e3\u67d0\u4e9b\u7535\u6c14\u7ec4\u5408\u8bbe\u5907\u7684\u771f\u5b9e\u884c\u4e3a\u201d\u3002\u5f53\u65f6\u739b\u4e3d\u5173\u6ce8\u5230\u4e86\u5176\u4e2d\u7684\u6570\u5b66\u95ee\u9898\uff0c\u4f46\u5374\u4e0d\u719f\u8bc6\u5176\u52a8\u529b\u5b66\u80cc\u666f\u3002\u4e8e\u662f\u5979\u53bb\u8bf7\u6559\u674e\u7279\u5c14\u4f0d\u5fb7\uff0c\u56e0\u4e3a\u4ed6\u5728\u7b2c\u4e00\u6b21\u4e16\u754c\u5927\u6218\u4e2d\u79ef\u7d2f\u4e86\u8bb8\u591a\u5173\u4e8e\u5bf9\u6297\u6218\u673a\u8fd0\u52a8\u8f68\u9053\u5206\u6790\u7684\u7ecf\u9a8c\u3002\u5979\u4fe9\u8ba8\u8bba\u4e86\u6587\u4ef6\u4e2d\u63d0\u53ca\u7531\u8303\u5fb7\u6ce2\u5c14\u57281920\u5e74\u63d0\u51fa\u7684\u5173\u4e8e\u65e0\u7ebf\u7535\u6ce2\u632f\u52a8\u95ee\u9898\u7684\u5fae\u5206\u65b9\u7a0b\uff1a<\/span><\/p>\n

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\u5176\u4e2d <\/span>k<\/span><\/em>, b<\/em>, \u03bb<\/em>, \u03b1<\/em>\u4e3a\u53c2\u6570\u3002\u8303\u5fb7\u6ce2\u5c14\u4e8e1927\u5e749\u6708\u5728\u300aNature\u300b\u6742\u5fd7\u4e0a\u53d1\u6587\u62a5\u544a\u4e86\u57fa\u4e8e\u8fd9\u4e2a\u5fae\u5206\u65b9\u7a0b\u7684\u9713\u8679\u706f\u5b9e\u9a8c\uff0c\u8bf4\u5f53\u9a71\u52a8\u4fe1\u53f7\u5177\u6709\u67d0\u79cd\u81ea\u7136\u9891\u7387\u65f6\uff0c\u4f1a\u542c\u5230\u201c\u6beb\u65e0\u89c4\u5f8b\u7684\u566a\u58f0\u201d\u3002\u8fd9\u7bc7\u6587\u7ae0\u5f88\u53ef\u80fd\u662f\u89c2\u5bdf\u5230\u7269\u7406\u6df7\u6c8c\u73b0\u8c61\u6700\u65e9\u7684\u5b9e\u9a8c\u62a5\u544a\uff0c\u53ea\u4e0d\u8fc7\u90a3\u65f6\u8fd8\u6ca1\u6709\u6df7\u6c8c\u8fd9\u4e2a\u6982\u5ff5\uff0c\u66f4\u8c08\u4e0d\u4e0a\u5176\u6570\u5b66\u7406\u8bba\u3002<\/span><\/p>\n

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\u56fe2  B. van der Pol and J. van der Mark, \u201cFrequency demultiplication\u201d, Nature, 1927<\/span><\/section>\n


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\u5f53\u5e74\uff0c\u739b\u4e3d\u548c\u674e\u7279\u5c14\u4f0d\u5fb7\u901a\u8fc7\u6570\u5b66\u5206\u6790\u53d1\u73b0\uff0c\u5de5\u7a0b\u5e08\u4eec\u5728\u96f7\u8fbe\u5236\u9020\u548c\u6d4b\u8bd5\u4e2d\u9047\u5230\u7684\u95ee\u9898\u5176\u5b9e\u5e76\u975e\u4eea\u5668\u8bbe\u5907\u7684\u8bbe\u8ba1\u548c\u5de5\u827a\u95ee\u9898\uff0c\u800c\u662f\u5fae\u5206\u65b9\u7a0b\u672c\u8eab\u7684\u6570\u5b66\u95ee\u9898\u3002\u5979\u4eec\u53d1\u73b0\u8fd9\u4e2a\u8c8c\u4f3c\u7b80\u5355\u7684\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u6709\u7740\u975e\u5e38\u590d\u6742\u7684\u52a8\u529b\u5b66\u7279\u6027\uff0c\u6709\u4e9b\u8fd8\u5f02\u4e4e\u5bfb\u5e38\u7684\u5947\u5f02\u3002\u4f8b\u5982\uff0c\u5979\u4eec\u53d1\u73b0\u8fd9\u4e2a\u65b9\u7a0b\u6709\u65e0\u7a77\u591a\u4e2a\u4e0d\u7a33\u5b9a\u7684\u5468\u671f\u89e3\u548c\u4e00\u4e2a\u9ad8\u5ea6\u590d\u6742\u7684\u7a33\u5b9a\u975e\u5468\u671f\u89e3\u7684\u5438\u5f15\u57df\u3002\u5979\u4eec\u4e25\u683c\u8bc1\u660e\u4e86\uff0c\u5f53 b<\/em>=0 \u65f6\uff0c\u968f\u7740<\/span> k<\/span><\/em>\u2192\u221e \uff0c\u8fd9\u4e2a\u65b9\u7a0b\u7684\u89e3\u8d8b\u5411\u4e8e\u552f\u4e00\u7684\u4e00\u6761\u5468\u671f\u8f68\u9053\u3002\u540e\u6765\uff0c\u53d7\u7f8e\u56fd\u6570\u5b66\u5bb6\u8bfa\u66fc\u00b7\u83b1\u6587\u68ee<\/span>\uff08Norman Levinson\uff0c1912-1975\uff09<\/span>\u76f8\u5173\u8bba\u6587\u7684\u5f71\u54cd\uff0c\u5979\u4eec\u628a\u62d3\u6251\u5b66\u7684\u601d\u60f3\u548c\u6280\u5de7\u5f15\u8fdb\u4e86\u5bf9\u4e00\u822c\u4e8c\u9636\u975e\u81ea\u6cbb\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u7684\u7814\u7a76\uff0c\u5e76\u53d1\u73b0\u975e\u5468\u671f\u89e3\u6709\u7740\u975e\u5e38\u8106\u5f31\u7684\u62d3\u6251\u7ed3\u6784\u3002\u5979\u4eec\u7684\u6210\u679c\u53cd\u8fc7\u6765\u53c8\u5e2e\u52a9\u89e3\u51b3\u4e86\u62d3\u6734\u5b66\u4e2d\u51e0\u4e2a\u60ac\u800c\u672a\u51b3\u7684\u95ee\u9898\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u7279\u522b\u5730\uff0c\u5979\u4eec\u8fd8\u6ce8\u610f\u5230\u4e86\u65b9\u7a0b\u521d\u59cb\u6761\u4ef6\u548c\u53c2\u6570\u7684\u4e0d\u9002\u5f53\u9009\u53d6\u4f1a\u5bfc\u81f4\u65b9\u7a0b\u89e3\u7684\u4e0d\u7a33\u5b9a\u6027\u548c\u4e0d\u53ef\u9884\u6d4b\u884c\u4e3a\uff0c\u8ba9\u5bf9\u5fae\u5206\u65b9\u7a0b\u7684\u5206\u6790\u548c\u6c42\u89e3\u53d8\u5f97\u6781\u5176\u56f0\u96be\u3002\u8fd9\u5176\u5b9e\u5c31\u662f\u540e\u6765\u4eba\u4eec\u8bf4\u7684\u201c\u8774\u8776\u6548\u5e94\u201d\u3002\u5979\u4eec\u7559\u4e0b\u4e86\u4e00\u4e2a\u201c\u5361\u7279\u8d56\u7279\u2014\u674e\u7279\u5c14\u4f0d\u5fb7\u731c\u60f3\u201d\uff1a\u8303\u5fb7\u6ce2\u5c14\u65b9\u7a0b\u5728 b<\/em> > 2\/3 \u65f6\u6709\u5e76\u4e14\u53ea\u6709\u4e00\u4e2a\u7a33\u5b9a\u7684\u5468\u671f\u89e3\u3002\u8fd9\u4e2a\u731c\u60f3\u540e\u6765\u57281972\u5e74\u7531\u82f1\u56fd\u6570\u5b66\u5bb6\u8bfa\u57c3\u5c14\u00b7\u52b3\u57c3\u5fb7<\/span>\uff08Noel G. Lloyd\uff0c1946-2019\uff09<\/span>\u8bc1\u5b9e\u3002<\/span><\/p>\n


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\u56fe3  M. L. Cartwright, \u201cForced oscillations in nonlinear systems,\u201d 1950.<\/span><\/section>\n


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\u63a5\u4e0b\u6765\u7684\u5341\u5e74\u95f4\uff0c\u739b\u4e3d\u81ea\u5df1\u4ee5\u53ca\u548c\u674e\u7279\u5c14\u4f0d\u5fb7\u5408\u4f5c\u53d1\u8868\u4e86\u4e00\u7cfb\u5217\u7684\u8bba\u6587\uff0c\u7ed9\u51fa\u4e86\u8f83\u4e3a\u4e00\u822c\u7684\u4e8c\u9636\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u7684\u5b58\u5728\u552f\u4e00\u6027\u3001\u6700\u7ec8\u6709\u754c\u6027\u4ee5\u53ca\u53ef\u80fd\u7684\u5468\u671f\u89e3\u3002\u4ed6\u4eec\u91c7\u7528\u4e86\u4e54\u6cbb\u00b7\u4f2f\u514b\u970d\u592b<\/span>\uff08George D. Birkhoff\uff0c1884-1944\uff09<\/span>\u7684\u89e3\u6790\u53d8\u6362\u65b9\u6cd5\uff0c\u5efa\u7acb\u4e86\u201c\u5361\u7279\u8d56\u7279\u2014\u674e\u7279\u5c14\u4f0d\u5fb7\u4e0d\u52a8\u70b9\u5b9a\u7406\u201d\uff0c\u53d1\u5c55\u4e86\u4e00\u5957\u5b8c\u6574\u4e25\u683c\u7684\u5fae\u5206\u7cfb\u7edf\u5f20\u5f1b\u632f\u8361\u6570\u5b66\u7406\u8bba\u3002\u90a3\u4e2a\u65f6\u6bb5\u5979\u4fe9\u8ba8\u8bba\u9891\u7e41\uff0c\u5e38\u5e38\u591c\u4ee5\u7ee7\u65e5\u3002\u5947\u7279\u7684\u662f\uff0c\u674e\u7279\u5c14\u4f0d\u5fb7\u559c\u6b22\u7528\u7eb8\u9762\u4e66\u5199\u800c\u4e0d\u662f\u9ed1\u677f\u6f14\u7b97\u7684\u65b9\u5f0f\u8ba8\u8bba\u6570\u5b66\u95ee\u9898\uff0c\u6b64\u5916\u4e5f\u559c\u6b22\u5728\u6563\u6b65\u65f6\u4f5c\u4ea4\u8c08\u8ba8\u8bba\u3002\u674e\u7279\u5c14\u4f0d\u5fb7\u540e\u6765\u56de\u5fc6\u8bf4\uff1a\u739b\u4e3d\u5f88\u7528\u529f\uff0c\u201c\u662f\u6211\u6bcf\u5929\u90fd\u8981\u5199\u7ed9\u5979\u4e24\u6b21[\u8ba8\u8bba\u7a3f]\u7684\u552f\u4e00\u5973\u6027\u201d\u3002<\/span><\/p>\n


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1939-1945\u5e74\u7b2c\u4e8c\u6b21\u4e16\u754c\u5927\u6218\u671f\u95f4\uff0c\u739b\u4e3d\u70ed\u60c5\u5730\u53c2\u4e0e\u4e86\u56fd\u9645\u7ea2\u5341\u5b57\u4f1a\u82f1\u56fd\u652f\u961f\u7684\u4e1a\u4f59\u670d\u52a1\u5de5\u4f5c\u3002<\/span><\/p>\n


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\u4f5c\u4e3a\u4e00\u4e2a\u5c0f\u63d2\u66f2\uff0c1945\u5e74\u739b\u4e3d\u7b80\u5316\u4e86\u67e5\u5c14\u65af\u00b7\u5384\u5bc6\u7279<\/span>\uff08Charles Hermite\uff0c1822\u20131901\uff09<\/span>\u7684\u521d\u7b49\u65b9\u6cd5\u8bc1\u660e\u4e86\u5706\u5468\u7387\u662f\u65e0\u7406\u6570\u3002\u8be5\u6f02\u4eae\u7684\u8bc1\u660e\u540e\u6765\u88ab\u54c8\u7f57\u5fb7\u00b7\u6770\u5f17\u91cc\u65af<\/span>\uff08Sir Harold Jeffreys\uff0c1891-1989\uff09<\/span>\u6536\u96c6\u5728\u540d\u8457\u300a\u79d1\u5b66\u63a8\u7406\u300b<\/span>\uff08Scientific Inference<\/em>\uff0c1974\uff09<\/span>\u7684\u9644\u5f55\u4e2d\u3002<\/span><\/p>\n


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\u5230\u4e861960\u5e74\u4ee3\uff0c\u739b\u4e3d\u5f00\u59cb\u7814\u7a76\u5468\u671f\u9a71\u52a8\u4e0b\u4e00\u822c\u4e8c\u9636\u975e\u81ea\u6cbb\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u7684\u201c\u51e0\u4e4e\u5468\u671f\u89e3\u201d<\/span>\uff08almost periodic solution\uff09<\/span>\uff0c\u5e76\u91c7\u7528\u6602\u5229\u00b7\u5e9e\u52a0\u83b1<\/span>\uff08Henri Poincar\u00e9\uff0c1854-1912\uff09<\/span>\u6620\u5c04\u53bb\u7814\u7a76\u51e0\u4e4e\u5468\u671f\u89e3\u6781\u9650\u70b9\u7684\u6700\u5c0f\u96c6\u3002\u5979\u8fd8\u628a\u5176\u4e2d\u4e00\u4e9b\u7ed3\u679c\u63a8\u5e7f\u5230\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u53bb\u30021964\u5e74\uff0c\u739b\u4e3d\u5728\u300a\u4f26\u6566\u6570\u5b66\u4f1a\u4f1a\u520a\u300b\u4e0a\u53d1\u8868\u4e86\u8457\u540d\u8bba\u6587\u201c\u4ece\u975e\u7ebf\u6027\u632f\u8361\u5230\u62d3\u6251\u52a8\u529b\u5b66\u201d<\/span>\uff08\u201cFrom non\u2013linear oscillations to topological dynamics\u201d\uff09<\/span>\u3002<\/span><\/p>\n


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\u81f3\u6b64\uff0c\u8bf4\u5230\u201c\u65e0\u7a77\u591a\u4e2a\u4e0d\u7a33\u5b9a\u7684\u5468\u671f\u89e3\u201d\u3001\u201c\u4e0d\u53ef\u9884\u6d4b\u6027\u201d\u548c\u201c\u51e0\u4e4e\u5468\u671f\u89e3\u201d\uff0c\u5c31\u79bb\u6df7\u6c8c\u7684\u73b0\u4ee3\u6570\u5b66\u7406\u8bba\u4e0d\u8fdc\u4e86\u3002<\/span><\/p>\n


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\u53d7\u5bfc\u5e08\u54c8\u4ee3\u7684\u5f71\u54cd\uff0c\u739b\u4e3d\u7684\u5174\u8da3\u8d77\u6e90\u4e8e\u7eaf\u6570\u5b66\uff0c\u66fe\u81ea\u8ba4\u4e3a\u662f\u4e2a\u7eaf\u6570\u5b66\u5bb6\u3002\u4f46\u662f\uff0c\u7814\u7a76\u4e86\u8303\u5fb7\u6ce2\u5c14\u5fae\u5206\u65b9\u7a0b\u4ee5\u540e\uff0c\u5979\u5f88\u611f\u6982\u5730\u8bf4\uff1a\u8fd9\u662f\u201c\u4e00\u4e2a\u5947\u7279\u7684\u3001\u7531\u4e0d\u540c\u5b66\u79d1\u548c\u4e0d\u540c\u80cc\u666f\u7684\u4eba\u5171\u540c\u53d1\u5c55\u8d77\u6765\u7684\u6570\u5b66\u5206\u652f\u2014\u2014\u5b83\u6db5\u76d6\u4e86\u7ecf\u5178\u529b\u5b66\u3001\u65e0\u7ebf\u7535\u632f\u8361\u3001\u7eaf\u6570\u5b66\u548c\u81ea\u52a8\u63a7\u5236\u7406\u8bba\u7684\u4f3a\u670d\u673a\u6784\u201d\u3002\u8bb8\u591a\u5e74\u4ee5\u540e\uff0c\u57281990\u5e74\u4ee3\u7684\u4e00\u6b21\u8bbf\u8c08\u4e2d\u5979\u8fd8\u8bf4\uff1a\u201c\u6211\u4fdd\u6301\u8fd9\u6837\u7684\u89c2\u70b9\uff0c\u5c31\u662f\u5728\u4e25\u683c\u62bd\u8c61\u63a8\u7406\u548c\u8003\u8651\u73b0\u5b9e\u601d\u7ef4\u4e4b\u95f4\u7684\u8fb9\u754c\u662f\u4e0d\u53ef\u80fd\u6e05\u6670\u5b9a\u4e49\u7684\u3002\u201d<\/span><\/p>\n


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\u56fe4  1932 \u4e16\u754c\u6570\u5b66\u5bb6\u5927\u4f1a\uff0c\u82cf\u9ece\u4e16 (\u53f3\u4e00\uff1a\u739b\u4e3d)<\/span><\/p>\n


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3. \u6df7\u6c8c\u6570\u5b66\u7406\u8bba\u7684\u6210\u578b<\/strong><\/strong><\/p>\n<\/section>\n

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\u739b\u4e3d\u662f\u4ee5\u201c\u672c\u6027\u8c26\u548c\u201d<\/span>\uff08characteristically modest\uff09<\/span>\u51fa\u540d\u7684\u4e00\u4f4d\u8c26\u865a\u4e25\u8c28\u7684\u6570\u5b66\u5bb6\u3002\u7406\u8bba\u7269\u7406\u5b66\u5bb6\u5f17\u91cc\u66fc\u00b7\u6234\u68ee<\/span>\uff08Freeman John Dyson\uff0c1923-2020\uff09<\/span>1942\u5e74\u5728\u5251\u6865\u5927\u5b66\u8bfb\u4e66\u65f6\u542c\u8fc7\u739b\u4e3d\u5173\u4e8e\u8303\u5fb7\u6ce2\u5c14\u5fae\u5206\u65b9\u7a0b\u7814\u7a76\u7684\u5b66\u672f\u62a5\u544a\uff0c\u5927\u53d7\u9f13\u821e\uff0c\u8ba4\u5b9a\u90a3\u662f\u6781\u5176\u6f02\u4eae\u7684\u6570\u5b66\u7ed3\u679c\u3002\u540e\u6765\uff0c\u6234\u68ee\u8bc4\u4ef7\u8bf4\uff1a\u674e\u7279\u5c14\u4f0d\u5fb7\u5e76\u4e0d\u7406\u89e3\u4ed6\u548c\u5361\u7279\u8d56\u7279\u6240\u505a\u7814\u7a76\u5de5\u4f5c\u7684\u6df1\u8fdc\u610f\u4e49\uff0c\u800c\u201c\u53ea\u6709\u5361\u7279\u8d56\u7279\u7406\u89e3\u5979\u7684\u5de5\u4f5c\u4f5c\u4e3a\u6df7\u6c8c\u7406\u8bba\u57fa\u7840\u7684\u91cd\u8981\u6027\u3002\u4f46\u5979\u4e0d\u662f\u4e00\u4e2a\u559c\u6b22\u4e3a\u81ea\u5df1\u5439\u5587\u53ed\u7684\u90a3\u79cd\u4eba\u3002\u201d<\/span>\uff08F. J. Dyson\uff0c\u201cMary Lucy Cartwright [1900-1998]\uff1aChaos theory\u201d\uff0c2010\uff09<\/span>\u3002<\/span><\/p>\n


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\u4e8b\u5b9e\u4e0a\uff0c\u739b\u4e3d\u5bf9\u6df7\u6c8c\u6570\u5b66\u7406\u8bba\u7684\u8d21\u732e\u4e00\u76f4\u90fd\u6ca1\u6709\u5f97\u5230\u8db3\u591f\u7684\u5173\u6ce8\uff0c\u76f4\u5230\u4e8c\u5341\u591a\u5e74\u540e\u7f8e\u56fd\u6570\u5b66\u5bb6\u65af\u8482\u82ac\u00b7\u65af\u6885\u5c14<\/span>\uff08Stephen Smale\uff0c1930\uff0d\uff09<\/span>\u53d1\u5c55\u4e86\u6df7\u6c8c\u6570\u5b66\u4e2d\u8457\u540d\u7684\u201c\u9a6c\u8e44\u7406\u8bba\u201d<\/span>\uff08Horseshoe theory\uff09<\/span>\u65f6\u624d\u5f97\u5230\u5370\u8bc1\u3002<\/span><\/p>\n


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\u65af\u6885\u5c14\u662f\u4e2a\u5f88\u6709\u6545\u4e8b\u7684\u4eba\uff0c\u5e76\u4e14\u4ed6\u7684\u540d\u58f0\u4e0d\u4ec5\u9650\u4e8e\u6570\u5b66\u3002\u4ed6\u8bf4\u4ed6\u6700\u597d\u7684\u4f5c\u54c1\u662f\u201c\u5728\u91cc\u7ea6<\/span>\uff08Rio\uff09<\/span>\u6d77\u6ee9\u4e0a\u201d\u5b8c\u6210\u7684\u30021960 \u5e74\uff0c\u65af\u6885\u5c14\u83b7\u5f97\u7f8e\u56fd\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u57fa\u91d1\u8d44\u52a9\u5230\u5df4\u897f\u91cc\u7ea6\u70ed\u5185\u5362\u505a\u535a\u58eb\u540e\u7814\u7a76\u3002\u65af\u6885\u5c14\u540e\u6765\u56de\u5fc6\u8bf4\uff0c\u4ed6\u5230\u8fbe\u91cc\u7ea6\u540e\u4e0d\u4e45\u53d1\u8868\u4e86\u4e00\u4efd\u624b\u7a3f\uff0c\u731c\u60f3\u201c\u6df7\u6c8c\u5e76\u4e0d\u5b58\u5728\u201d\u3002\u4f46\u662f\u5f88\u5feb\uff0c\u4ed6\u6536\u5230\u4e86\u8d44\u6df1\u6570\u5b66\u5bb6\u8bfa\u66fc\u00b7\u83b1\u6587\u68ee\u7684\u4e00\u5c01\u6765\u4fe1\uff0c\u7ed9\u4ed6\u4e3e\u4e86\u4e2a\u53cd\u4f8b\uff0c\u5e76\u5efa\u8bae\u4ed6\u53bb\u770b\u5361\u7279\u8d56\u7279-\u674e\u7279\u5c14\u4f0d\u5fb7\u7684\u6587\u7ae0\u3002\u65af\u6885\u5c14\u5728\u91cc\u7ea6\u6d77\u6ee9\u4e0a\u8eba\u4e86\u5f88\u4e45\uff0c\u53cd\u590d\u7422\u78e8\u3002\u201c\u901a\u8fc7\u8fd9\u4e9b\u601d\u8003\u8fc7\u7a0b\uff0c\u6211\u6700\u7ec8\u8bf4\u670d\u4e86\u6211\u81ea\u5df1\u3002\u73b0\u5728\u6211\u8ba4\u4e3a\u83b1\u6587\u68ee\u786e\u5b9e\u662f\u5bf9\u7684\uff0c\u800c\u6211\u7684\u731c\u60f3\u662f\u9519\u7684\u3002\u6df7\u6c8c\u5df2\u7ecf\u9690\u542b\u5728\u5361\u7279\u8d56\u7279\u548c\u674e\u7279\u5c14\u4f0d\u5fb7\u7684\u5206\u6790\u4e2d\u3002\u6096\u8bba\u89e3\u51b3\u4e86\uff0c\u662f\u6211\u731c\u9519\u4e86\u3002\u4f46\u662f\u5728\u8fd9\u5b66\u4e60\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u53d1\u73b0\u4e86\u9a6c\u8e44\uff01\u201d \u4ece\u6b64\u4ee5\u540e\uff0c\u6570\u5b66\u754c\u6709\u4e86\u73b0\u4ee3\u6df7\u6c8c\u7406\u8bba\u7684\u4e00\u5757\u57fa\u77f3\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u4e5f\u542f\u53d1\u4e86\u65af\u6885\u5c14\u5728\u5927\u4e8e 4 \u7684\u7ef4\u5ea6\u4e0a\u89e3\u51b3\u4e86\u5e9e\u52a0\u83b1\u731c\u60f3\uff0c\u8ba9\u4ed6\u57281966\u5e74\u8363\u81ba\u83f2\u5c14\u5179\u5956<\/span>\uff08Fields Medal\uff09<\/span>\u3002<\/span><\/p>\n


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\u8bf4\u5230\u6cd5\u56fd\u6570\u5b66\u5bb6\u5e9e\u52a0\u83b1\uff0c\u4ed6\u88ab\u8ba4\u4e3a\u662f\u201c\u5386\u53f2\u4e0a\u6700\u540e\u4e00\u4e2a\u6570\u5b66\u901a\u624d\u201d\u30021887\u5e74\uff0c\u745e\u5178\u56fd\u738b\u5965\u65af\u5361\u4e8c\u4e16<\/span>\uff08Oskar, II\uff09<\/span>\u60ac\u8d4f\uff0c\u5f81\u6c42\u592a\u9633\u7cfb\u7a33\u5b9a\u6027\u95ee\u9898\u7684\u89e3\u7b54\uff0c\u671f\u671b\u89e3\u51b3\u5929\u4f53\u529b\u5b66\u4e2d\u7684 N \u4f53\u95ee\u9898\u3002\u5e9e\u52a0\u83b1\u4ee5\u4ed6\u7684\u4e09\u4f53\u95ee\u9898\u7814\u7a76\u6210\u679c\u83b7\u5f97\u4e86\u5927\u5956\u3002\u53ef\u662f\uff0c\u8bba\u6587\u88ab\u9001\u5230\u300aActa Mathematica\u300b\u6742\u5fd7\u4ed8\u5370\u65f6\uff0c\u9752\u5e74\u6570\u5b66\u7f16\u8f91\u62c9\u65af\u00b7\u7b26\u6587<\/span>\uff08Lars E. Phragm\u00e9n\uff0c1863-1937\uff09<\/span>\u5728\u6821\u5bf9\u8fc7\u7a0b\u4e2d\u53d1\u73b0\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u4fbf\u53bb\u54a8\u8be2\u5e9e\u52a0\u83b1\u3002\u5e9e\u52a0\u83b1\u660e\u767d\u4e86\u90a3\u662f\u4e2a\u57fa\u672c\u9519\u8bef\u3002\u6df1\u601d\u719f\u8651\u4e4b\u540e\uff0c\u5e9e\u52a0\u83b1\u5f7b\u5e95\u5730\u6539\u53d8\u4e86\u539f\u6765\u91c7\u7528\u7684\u4f20\u7edf\u5b9a\u91cf\u5206\u6790\u65b9\u6cd5\uff0c\u4ee5\u5b9a\u6027\u5206\u6790\u91cd\u65b0\u63a2\u8ba8\u4e86\u8fd9\u4e2a\u6570\u5b66\u4e0a\u6781\u5176\u8270\u6df1\u7684\u95ee\u9898\u3002\u5176\u4e2d\uff0c\u5e9e\u52a0\u83b1\u53d1\u73b0\u4e86\u975e\u7ebf\u6027\u7cfb\u7edf\u89e3\u7684\u540c\u5bbf\u8f68\u9053\u7f20\u7ed5\u73b0\u8c61\uff0c\u540e\u4eba\u77e5\u9053\u90a3\u662f\u6df7\u6c8c\u7684\u6700\u4e3b\u8981\u7279\u5f81\u4e4b\u4e00\u3002\u5e9e\u52a0\u83b1\u7684\u8bba\u6587\u4fee\u6539\u597d\u540e\u5728\u8be5\u6742\u5fd7\u4e8e1890\u5e74\u6b63\u5f0f\u53d1\u8868\uff0c\u4ece\u6b64\u63a8\u52a8\u4e86\u6570\u5b66\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u3001\u7279\u522b\u662f\u6df7\u6c8c\u7406\u8bba\u7684\u84ec\u52c3\u53d1\u5c55\u3002\u5e9e\u52a0\u83b1\u5728\u300a\u79d1\u5b66\u4e0e\u65b9\u6cd5\u300b<\/span>\uff08Science et M\u00e9thode<\/em>\uff0c1908 \uff09<\/span>\u4e00\u4e66\u4e2d\u56de\u5fc6\u8bf4\uff0c\u5f53\u65f6\u53d1\u73b0\u4e86\u201c\u521d\u59cb\u6761\u4ef6\u7684\u5fae\u5c0f\u8bef\u5dee\u5728\u6700\u540e\u7ed3\u679c\u4e2d\u4ea7\u751f\u6781\u5927\u5dee\u522b\u7684\u60c5\u51b5\u4f1a\u53d1\u751f\u2026\u2026 \u4e8e\u662f\u9884\u6d4b\u53d8\u5f97\u4e0d\u53ef\u80fd\uff0c\u4ece\u800c\u6211\u4eec\u5c31\u770b\u5230\u4e86\u8bb8\u591a\u4f3c\u4e4e\u662f\u5076\u7136\u7684\u8868\u9762\u73b0\u8c61\u201d\u3002<\/span><\/p>\n


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\u72ec\u7acb\u4e8e\u5e9e\u52a0\u83b1\uff0c\u4fc4\u7f57\u65af\u5973\u6570\u5b66\u5bb6\u7d22\u83f2\u5a05\u00b7\u67ef\u74e6\u5217\u592b\u65af\u5361\u5a05<\/span>\uff08Sonya Kovalevskaya\uff0c1850-1891\uff09<\/span>\u4e5f\u6307\u51fa\u8fc7\u8bb8\u591a\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u662f\u4e0d\u53ef\u80fd\u6c42\u51fa\u7cbe\u786e\u89e3\u6790\u89e3\u7684\uff0c\u867d\u7136\u5979\u81ea\u5df1\u66fe\u7528\u8d85\u692d\u5706\u51fd\u6570\u7ed9\u51fa\u4e86\u4e09\u4f53\u95ee\u9898\u4e2d\u4e09\u4e2a\u7279\u522b\u60c5\u5f62\u7684\u89e3\u6790\u89e3\u3002\u67ef\u74e6\u5217\u592b\u65af\u5361\u5a05\u662f\u5386\u53f2\u4e0a\u7b2c\u4e00\u4e2a\u5973\u6570\u5b66\u535a\u58eb\uff0c1874\u5e74\u5728\u5fb7\u56fd\u54e5\u5ef7\u6839\u6bd5\u4e1a\uff0c\u662f\u5361\u5c14\u00b7\u9b4f\u5c14\u65af\u7279\u62c9\u65af<\/span>\uff08Karl T. W. Weierstrass\uff0c1815-1897\uff09<\/span>\u7684\u5b66\u751f\uff0c1889\u5e74\u5728\u745e\u5178Stockholm\u5927\u5b66\u4efb\u8058\u6210\u4e3a\u4e16\u754c\u4e0a\u7b2c\u4e00\u4f4d\u5973\u6559\u6388\u3002\u5341\u5206\u53ef\u60dc\u7684\u662f\uff0c\u597941\u5c81\u65f6\u611f\u67d3\u6d41\u611f\u4e0d\u6cbb\uff0c\u4e0d\u5e78\u79bb\u4e16\u3002<\/span><\/p>\n


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\u591a\u5e74\u4e4b\u540e\uff0c\u57281954\u5e74\u4e16\u754c\u6570\u5b66\u5bb6\u5927\u4f1a\u95ed\u5e55\u5f0f\u62a5\u544a\u91cc\uff0c\u82cf\u8054\u6570\u5b66\u5bb6\u5b89\u5fb7\u70c8\u00b7\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b<\/span>\uff08Andrey N. Kolmogorov\uff0c1903\u20131987\uff09<\/span>\u4e0d\u52a0\u8bc1\u660e\u5730\u53d9\u8ff0\u4e86\u4e00\u4e2a\u5b9a\u7406\uff0c\u8bd5\u56fe\u89e3\u91ca\u6d6e\u70b9\u8fd0\u7b97\u89c2\u5bdf\u4e0d\u5230\u7684\u6df7\u6c8c\u73b0\u8c61\u3002\u540e\u6765\uff0c\u5f17\u62c9\u57fa\u7c73\u5c14\u00b7\u963f\u8bfa\u5fb7<\/span>\uff08Vladimir I. Arnold\uff0c1937-2010\uff09<\/span>\u548c\u5c24\u5c14\u6839\u00b7\u83ab\u6cfd\u5c14<\/span> (J\u00fcrgen K. Moser, 1928\u20131999\uff09<\/span>\u8865\u5145\u4e86\u5168\u90e8\u7684\u7ec6\u8282\uff0c\u5171\u540c\u5efa\u7acb\u4e86\u8457\u540d\u7684Kolmogorov-Arnold-Moser<\/span>\uff08KAM\uff09<\/span>\u5b9a\u7406\u3002\u8be5\u5b9a\u7406\u6307\u51fa\uff0c\u5fae\u5c0f\u6270\u52a8\u4e4b\u4e0b\u53ef\u79ef\u7cfb\u7edf\u7684\u73af\u9762\u53ea\u4f1a\u53d8\u5f62\u800c\u4e0d\u4f1a\u6d88\u5931\uff1b\u4f46\u5982\u679c\u6709\u73af\u9762\u53d7\u5230\u7834\u574f\u7684\u8bdd\uff0c\u5b83\u4fbf\u4f1a\u5bfc\u81f4\u6df7\u6c8c\u3002\u8fd9\u4e00\u6df7\u6c8c\u4ea7\u751f\u8fc7\u7a0b\u7c7b\u4f3c\u4e8e\u65af\u6885\u5c14\u9a6c\u8e44\u6620\u5c04\u3002\u540e\u4eba\u8fd8\u628aKAM\u5b9a\u7406\u5e94\u7528\u5230\u592a\u9633\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u5206\u6790\u3002<\/span><\/p>\n


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\u81ea\u5e9e\u52a0\u83b1\u4ee5\u6765\uff0c\u8bb8\u591a\u6570\u5b66\u5bb6\u4f3c\u4e4e\u5df2\u7ecf\u770b\u5230\u4e86\u6df7\u6c8c\u5b58\u5728\u7684\u5e7d\u7075\uff0c\u4f46\u59cb\u7ec8\u6ca1\u6709\u4eba\u7ed9\u51fa\u4e00\u4e2a\u5177\u4f53\u7684\u5fae\u5206\u65b9\u7a0b\u4f8b\u5b50\u3002<\/span><\/p>\n


<\/span><\/p>\n

1963\u5e74\uff0c\u5927\u6c14\u7269\u7406\u5b66\u5bb6\u7231\u5fb7\u534e\u00b7\u6d1b\u4f26\u8328<\/span>\uff08Edward N. Lorenz\uff0c1917-2008\uff09<\/span>\u51fa\u573a\u4e86\uff0c\u7ed9\u51fa\u4e86\u4eca\u5929\u5e7f\u4e3a\u4eba\u77e5\u7684\u4e09\u7ef4\u4e00\u9636\u81ea\u6cbb<\/span>\uff08\u4e8c\u6b21\u591a\u9879\u5f0f\uff09<\/span>\u5fae\u5206\u65b9\u7a0b\u7cfb\u7edf\uff0c\u5373\u8457\u540d\u7684\u6d1b\u4f26\u8328\u7cfb\u7edf\uff0c\u5e76\u5728\u6570\u503c\u8ba1\u7b97\u4e2d\u89c2\u5bdf\u5230\u4e86\u201c\u6df7\u6c8c\u5438\u5f15\u5b50\u201d<\/span>\uff08chaotic attractor\uff09<\/span>\uff08<\/span>\u53c2\u89c1\u5f80\u671f\u6587\u7ae0\u300a\u8774\u8776\u6548\u5e94\u548c\u6df7\u6c8c\u6545\u4e8b | \u9648\u5173\u8363<\/a><\/span>\u300b\uff09<\/span>\u3002\u5f53\u7136\uff0c\u5bf9\u6bd4\u4e4b\u540e\uff0c\u4eba\u4eec\u5f88\u5feb\u5c31\u60f3\u5230\u4e86\u8303\u5fb7\u6ce2\u5c14\u65b9\u7a0b\uff0c\u5b83\u5176\u5b9e\u7b49\u4ef7\u4e8e\u4e00\u4e2a\u4e09\u7ef4\u4e00\u9636\u81ea\u6cbb<\/span>\uff08\u975e\u591a\u9879\u5f0f\uff09<\/span>\u5fae\u5206\u65b9\u7a0b\u7cfb\u7edf\u3002\u6d1b\u4f26\u8328\u5728\u4ed6\u300a\u6df7\u6c8c\u7684\u672c\u8d28\u300b<\/span>\uff08The Essence of Chaos<\/em>\uff0c1995\uff09<\/span>\u4e00\u4e66\u4e2d\u4e5f\u63d0\u5230\u4e86\u5361\u7279\u8d56\u7279\u548c\u674e\u7279\u5c14\u4f0d\u5fb7\u7684\u6570\u5b66\u5206\u6790\u5bf9\u6df7\u6c8c\u7406\u8bba\u53d1\u5c55\u7684\u91cd\u8981\u5f71\u54cd\u3002\u540e\u6765\u77e5\u9053\uff0c\u6bd4\u6d1b\u4f26\u8328\u7565\u65e9\u7684\u8fd8\u6709\u65e5\u672c\u4eac\u90fd\u5927\u5b66\u7684\u7535\u5b50\u5de5\u7a0b\u5b66\u6559\u6388\u4e0a\u7530\u7746\u4eae<\/span>\uff08Yoshisuke Ueda\uff0c1936\u2013 \uff09<\/span>\uff0c\u4ed6\u57281961\u5e74\u5c1a\u662f\u4e2a\u7814\u7a76\u751f\u65f6\u5c31\u4ece\u5b9e\u9a8c\u5ba4\u91cc\u89c2\u5bdf\u8bb0\u5f55\u4e86\u65b9\u7a0b<\/span><\/p>\n

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\u5f53 k<\/em>=0.2, h<\/em>=8, b<\/em>=0.35, <\/span>\u03b1<\/span><\/em>=1.02\u65f6\u7684\u6df7\u6c8c\u5438\u5f15\u5b50\uff0c\u79f0\u4e3a\u65e5\u672c\u5438\u5f15\u5b50<\/span>\uff08Japanese attractor\uff09<\/span>\u3002\u4e0d\u8fc7\uff0c\u540e\u6765\u4ed6\u81ea\u5df1\u4e5f\u77e5\u9053\uff0c\u8fd9\u4e2a\u65b9\u7a0b\u6bd4\u675c\u82ac<\/span>\uff08Georg Duffing\uff0c1861\u20131944\uff09<\/span>\u6df7\u6c8c\u65b9\u7a0b\u8fd8\u8981\u590d\u6742\u4e00\u4e9b\u3002<\/span><\/p>\n


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\u56fe5  \u6d1b\u4f26\u8328\u6df7\u6c8c\u5438\u5f15\u5b50<\/span><\/p>\n


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\u524d\u9762\u8bf4\u5230\u7684\u6df7\u6c8c\u7cfb\u7edf\u90fd\u662f\u65f6\u95f4\u8fde\u7eed\u5fae\u5206\u65b9\u7a0b\u30021975\u5e74\uff0c\u674e\u5929\u5ca9<\/span>\uff08Tien-Yien Li\uff0c1945-2020\uff09<\/span>\u548c\u8a79\u59c6\u65af\u00b7\u7ea6\u514b<\/span>\uff08Jams A. Yorke\uff0c1941\uff0d\uff09<\/span>\u53d1\u8868\u4e86\u4e00\u7bc7\u9898\u4e3a\u201c\u5468\u671f\u4e09\u610f\u5473\u7740\u6df7\u6c8c\u201d\u7684\u6587\u7ae0\uff0c\u8ba8\u8bba\u4e86\u6d1b\u4f26\u8328\u7684\u6c14\u8c61\u7cfb\u7edf\u548c\u7f57\u4f2f\u7279\u00b7\u6885<\/span>\uff08Robert M. May\uff0c1936-2020\uff09<\/span>\u7684Logistic\u6620\u5c04\uff0c\u8bc1\u660e\u4e86\u4e00\u6761\u6f02\u4eae\u7684\u6570\u5b66\u5b9a\u7406\uff0c\u5f00\u542f\u4e86\u79bb\u6563\u6df7\u6c8c\u6570\u5b66\u7406\u8bba\u7684\u5148\u6cb3<\/span>\uff08\u53c2\u89c1\u5f80\u671f\u6587\u7ae0\u300a\u79bb\u6563\u6df7\u6c8c\u4f20\u5947\u4e28\u9648\u5173\u8363<\/a>\u300b\uff09<\/span>\u3002\u540e\u6765\uff0c\u5f17\u91cc\u66fc\u00b7\u6234\u68ee\u5728\u4ed62009\u5e74\u521d\u7531\u300a\u7f8e\u56fd\u6570\u5b66\u4f1a\u4f1a\u520a\u300b\u53d1\u8868\u5e76\u5728\u201c\u7231\u56e0\u65af\u5766\u8bb2\u5ea7\u201d\u4e0a\u6f14\u8bb2\u7684\u8457\u540d\u6587\u7ae0\u201c\u9e1f\u4e0e\u86d9\u201d<\/span>\uff08Birds and Frogs\uff09<\/span>\u4e2d\u8bf4\uff1a\u201c\u5728\u6df7\u6c8c\u5b66\u7684\u9886\u57df\u4e2d\uff0c\u6211\u77e5\u9053\u7684\u53ea\u6709\u4e00\u6761\u4e25\u683c\u8bc1\u660e\u4e86\u7684\u5b9a\u7406\uff0c\u90a3\u662f\u7531\u674e\u5929\u5ca9\u548c\u8a79\u59c6\u65af\u00b7\u7ea6\u514b\u57281975\u5e74\u53d1\u8868\u7684\u4e00\u7bc7\u77ed\u6587\u2018\u5468\u671f\u4e09\u610f\u5473\u7740\u6df7\u6c8c\u2019\u4e2d\u6240\u5efa\u7acb\u7684\u3002\u201d \u4ed6\u5c06\u674e\u2013\u7ea6\u514b\u8fd9\u7bc7\u8bba\u6587\u8a89\u4e3a\u201c\u6570\u5b66\u6587\u732e\u4e2d\u4e0d\u673d\u7684\u73cd\u54c1\u4e4b\u4e00\u201d\u3002<\/span><\/p>\n


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\u56fe6   \u53ef\u7528Li-Yorke \u5b9a\u7406\u8bc1\u660e\u7684\u6df7\u6c8cLogistic\u6620\u5c04\uff1a<\/span><\/p>\n

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4. \u6210\u540d\u4e4b\u540e<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


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1947\u5e74\uff0c\u739b\u4e3d\u88ab\u9009\u4e3a\u82f1\u56fd\u7687\u5bb6\u5b66\u4f1a\u9662\u58eb\uff0c\u662f\u7687\u5bb6\u5b66\u4f1a1660\u5e74\u6210\u7acb\u4ee5\u6765\u7684\u7b2c\u4e00\u4e2a\u5973\u6570\u5b66\u9662\u58eb\u3002\u5979\u540e\u6765\u8fd8\u662f\u7687\u5bb6\u5b66\u4f1a\u7406\u4e8b\u4f1a\u5386\u53f2\u4e0a\u7684\u7b2c\u4e00\u4f4d\u5973\u7406\u4e8b\u3002<\/span><\/p>\n


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1949\u5e74\u521d\uff0c\u5979\u5e94\u9080\u5230\u7f8e\u56fd\u8fdb\u884c\u5b66\u672f\u8bbf\u95ee\uff0c\u5148\u540e\u5230\u4e86\u65af\u5766\u798f\u3001UCLA\u548c\u666e\u6797\u65af\u987f\u4f5c\u975e\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u5b9a\u6027\u5206\u6790\u7684\u7cfb\u5217\u6f14\u8bb2\u3002<\/span><\/p>\n


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1949\u5e74\u4ece\u7f8e\u56fd\u56de\u5230\u5251\u6865\u4e4b\u540e\uff0c\u739b\u4e3d\u53d6\u5f97\u4e86\u5251\u6865\u79d1\u5b66\u535a\u58eb<\/span>\uff08ScD\uff09<\/span>\u5b66\u4f4d\u5e76\u88ab\u9009\u4e3a\u683c\u987f\u5973\u5b50\u5b66\u9662\u7684\u9662\u957f<\/span>\uff08Mistress of Girton College\uff09<\/span>\u3002\u5979\u8bf4\u90a3\u662f\u201c\u5b9e\u9645\u4e0a\u4e0d\u53ef\u63a8\u8131\u7684\u9009\u4e3e\u201d\u7ed3\u679c\u3002<\/span><\/p>\n


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1950\u5e74\uff0c\u5979\u51fa\u4efb\u82f1\u56fd\u6570\u5b66\u4f1a\u4e3b\u5e2d\u3002<\/span><\/p>\n


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\u5176\u540e\uff0c\u5979\u8fd8\u517c\u4efb\u4e86\u591a\u79cd\u5b66\u672f\u548c\u884c\u653f\u59d4\u5458\u4f1a\u804c\u52a1\uff0c\u7279\u522b\u662f\u91cd\u8981\u800c\u7e41\u7410\u7684\u5251\u6865\u5973\u5458\u5de5\u4efb\u804c\u59d4\u5458\u4f1a\u4e3b\u5e2d\u3001\u5251\u6865\u5987\u5973\u8054\u5408\u4f1a\u4e3b\u5e2d\u3001\u5251\u6865\u6559\u5de5\u59d4\u5458\u4f1a\u4e3b\u5e2d\u3001\u4ee5\u53ca\u4e24\u5c4a\u5251\u6865\u5927\u5b66\u53c2\u8bae\u4f1a\u7406\u4e8b\u3002\u5979\u6162\u6162\u5730\u628a\u4e3b\u8981\u7cbe\u529b\u6295\u5165\u5230\u4e86\u6570\u5b66\u6559\u80b2\u548c\u5b66\u6821\u884c\u653f\u4e8b\u52a1\u4e2d\u3002\u5979\u4e3a\u4eba\u6e29\u6587\u5c14\u96c5\u3001\u529e\u4e8b\u516c\u6b63\u4e25\u8c28\uff0c\u6df1\u53d7\u5e08\u751f\u4eec\u7684\u7231\u6234\u3002<\/span><\/p>\n


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\u5c3d\u7ba1\u5982\u6b64\uff0c\u739b\u4e3d\u5728\u4f59\u751f\u4e00\u76f4\u6ca1\u6709\u505c\u6b62\u6570\u5b66\u7814\u7a76\u3002\u5979\u7ee7\u7eed\u7814\u7a76\u5fae\u5206\u65b9\u7a0b\u7684\u65b0\u9896\u62d3\u6251\u65b9\u6cd5\uff0c\u5e76\u5728\u51fd\u6570\u7406\u8bba\u4ee5\u53ca\u7c07\u96c6\u7406\u8bba\u7b49\u65b9\u9762\u65f6\u6709\u65b0\u4f5c\u3002\u540c\u65f6\uff0c\u5979\u8fd8\u5199\u4e86\u4e00\u7cfb\u5217\u7684\u6587\u732e\u7efc\u8ff0\u548c\u7814\u7a76\u5c55\u671b\u6587\u7ae0\uff0c\u5176\u4e2d\u7279\u522b\u8457\u540d\u7684\u662f\u5173\u4e8e1920-1930\u5e74\u95f4\u53d1\u5c55\u8d77\u6765\u7684\u201cHardy-Littlewood-Paley-Riesz circle\u201d\u7406\u8bba\u7684\u5386\u53f2\u56de\u987e\u548c\u8bc4\u8bba\uff0c\u4ee5\u53ca\u5f88\u6709\u5f71\u54cd\u7684\u79d1\u666e\u4e66\u300a\u6570\u5b66\u601d\u7ef4\u300b<\/span>\uff08\u201cThe Mathematical Mind\u201d\uff0c1955\uff09<\/span>\u548c\u4e13\u8457\u300a\u79ef\u5206\u51fd\u6570\u300b<\/span>\uff08\u201cIntegral Functions\u201d\uff0c1956\uff09<\/span>\u3002<\/span><\/p>\n


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1956\u5e74\uff0c\u5979\u4f5c\u4e3a\u82f1\u56fd\u7687\u5bb6\u5b66\u4f1a\u6210\u5458\u968f\u4ee3\u8868\u56e2\u8bbf\u95ee\u4e86\u82cf\u8054\u548c\u6ce2\u5170\uff0c\u5230\u8fc7\u83ab\u65af\u79d1\u5927\u5b66\u548c\u6ce2\u5170\u79d1\u5b66\u9662\u5e76\u53c2\u52a0\u4e86\u5b66\u672f\u4f1a\u8bae\u3002<\/span><\/p>\n


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\u739b\u4e3d\u4e8e1959\u5e74\u664b\u5347\u4e3a\u5251\u6865\u5927\u5b66\u51fd\u6570\u7406\u8bba\u6559\u6388<\/span>\uff08Reader\uff09<\/span>\uff0c1961-1963\u5e74\u62c5\u4efb\u4f26\u6566\u6570\u5b66\u4f1a\u4e3b\u5e2d\uff0c1968\u5e74\u9000\u4f11\u3002<\/span><\/p>\n


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\u5176\u5b9e\u739b\u4e3d\u9000\u800c\u4e0d\u4f11\uff0c\u5979\u4e0d\u505c\u6b47\u5730\u7ee7\u7eed\u5979\u7684\u5b66\u672f\u4ea4\u6d41\u6d3b\u52a8\u548c\u6570\u5b66\u7814\u7a76\u30021970\u5e74\u4ee3\uff0c\u5979\u548c\u5251\u6865\u6570\u5b66\u5bb6\u4ea8\u5229\u00b7\u65af\u5a01\u7eb3\u987f-\u6234\u5c14<\/span>\uff08Sir Henry P. F. Swinnerton-Dyer\uff0c1927-2018\uff09<\/span>\u7ef4\u6301\u4e86\u957f\u8fbe\u5341\u5e74\u7684\u5408\u4f5c\uff0c\u4e3b\u8981\u7814\u7a76\u4e8c\u9636\u5fae\u5206\u65b9\u7a0b\u7684\u6709\u754c\u6027\u3002\u671f\u95f4\uff0c\u5979\u8fd8\u53c2\u4e0e\u4e86\u4f26\u6566\u6570\u5b66\u4f1a\u59d4\u6258\u7684\u300a\u54c8\u4ee3\u8bba\u6587\u96c6\u300b<\/span>\uff08The Collected Papers of G. H. Hardy\uff0c1974\uff09<\/span>\u7684\u7f16\u8f91\u5de5\u4f5c\u3002<\/span><\/p>\n


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\u56fe7  \u739b\u4e3d\u00b7\u5361\u7279\u8d56\u7279\uff08\u5251\u6865\u683c\u987f\u5b66\u9662\uff09<\/span><\/p>\n


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\u739b\u4e3d\u5148\u540e\u83b7\u5f97Edinburgh\u3001Leeds\u3001Hull\u3001Wales \u548c Oxford \u5927\u5b66\u7684\u8363\u8a89\u535a\u58eb\u5b66\u4f4d\uff0c\u4ee5\u53caFinland\u5927\u5b66\u7684\u8363\u8a89\u52cb\u7ae0\u30021964\u5e74\uff0c\u5979\u4f5c\u4e3a\u7b2c\u4e00\u4f4d\u5973\u6027\u6570\u5b66\u5bb6\u83b7\u5f97\u4e86\u4f26\u6566\u7687\u5bb6\u5b66\u4f1a\u6700\u9ad8\u8363\u8a89\u7684Sylvester \u91d1\u8d28\u5956\u7ae0\u30021968\u5e74\uff0c\u5979\u88ab\u6388\u4e88\u7231\u4e01\u5821\u7687\u5bb6\u5b66\u9662\u8363\u8a89\u9662\u58eb\uff0c\u540c\u5e74\u53c8\u4f5c\u4e3a\u7b2c\u4e00\u4f4d\u5973\u6027\u6570\u5b66\u5bb6\u83b7\u5f97\u4e86\u4f26\u6566\u6570\u5b66\u4f1a\u6700\u9ad8\u8363\u8a89\u7684 de Morgan \u91d1\u8d28\u5956\u7ae0\u30021969\u5e74\uff0c\u5979\u88ab\u5973\u738b\u4f0a\u4e3d\u838e\u767d\u4e8c\u4e16\u518c\u5c01\u4e3a\u82f1\u56fd\u7687\u5bb6\u5973\u7235\u58eb<\/span>\uff08Dame Commander of the British Empire\uff09<\/span>\u3002<\/span><\/p>\n


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\u739b\u4e3d\u00b7\u5361\u7279\u8d56\u7279\u4e00\u8f88\u5b50\u5355\u8eab\uff0c\u559c\u6b22\u5916\u51fa\u5b66\u672f\u8bbf\u95ee\uff0c\u6781\u5177\u5e7d\u9ed8\u611f\u548c\u540c\u60c5\u5fc3\uff0c\u665a\u5e74\u81ea\u6211\u9676\u9189\u4e8e\u7ed8\u753b\u548c\u97f3\u4e50\u3002\u5979\u4e8e1998\u5e744\u67083\u65e5\u5728\u82f1\u56fd\u5251\u6865\u7684 Midfield Lodge \u517b\u8001\u9662\u8f9e\u4e16\uff0c\u4eab\u5e7498\u5c81\u3002<\/span><\/p>\n


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\u4e3a\u4e86\u7eaa\u5ff5\u739b\u4e3d\uff0c\u4f26\u6566\u6570\u5b66\u4f1a\u8bbe\u7acb\u4e86\u5e74\u5ea6\u201c\u739b\u4e3d\u00b7\u5361\u7279\u8d56\u7279\u8bb2\u5ea7\u201d<\/span>\uff08Mary Cartwright Lecture\uff09<\/span>\u7cfb\u5217\uff0c\u6f14\u8bb2\u4eba\u5747\u7531\u201c\u5973\u6570\u5b66\u5bb6\u59d4\u5458\u4f1a\u201d<\/span>\uff08Women in Mathematics Committee\uff09<\/span>\u63d0\u540d\u9080\u8bf7\u3002<\/span><\/p>\n


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\u739b\u4e3d\u4e00\u751f\u6709\u8bb8\u591a\u9ad8\u6df1\u6f02\u4eae\u7684\u6570\u5b66\u6210\u679c\uff0c\u88ab\u5199\u8fdb\u4e8690\u591a\u7bc7\u4f18\u96c5\u6d41\u7545\u7684\u5b66\u672f\u8bba\u8457\u4e2d\u3002\u5979\u5e38\u5e38\u88ab\u95ee\u5230\uff1a\u4f60\u6709\u8fd9\u4e48\u591a\u597d\u8bba\u6587\uff0c\u81ea\u5df1\u6700\u6b23\u8d4f\u7684\u662f\u54ea\u4e00\u7bc7\u5462\uff1f\u739b\u4e3d\u6bcf\u6b21\u90fd\u4e0d\u7ecf\u601d\u8003\u5730\u56de\u590d\u540c\u4e00\u53e5\u8bdd\uff1a\u201c\u5662\uff0c\u662f\u6211\u624b\u5934\u4e0a\u6b63\u5728\u5199\u7684\u8fd9\u4e00\u7bc7\u3002\u201d<\/span><\/p>\n


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\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science<\/span>\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/span>
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