{"id":3615,"date":"2012-02-09T20:07:14","date_gmt":"2012-02-09T12:07:14","guid":{"rendered":"http:\/\/wamath.sinaapp.com\/?p=1795"},"modified":"2012-02-09T20:07:14","modified_gmt":"2012-02-09T12:07:14","slug":"%e4%b9%b1%e8%b0%88peter-walters%e3%80%8aan-introduction-to-ergodic-theory%e3%80%8b%e5%bf%85%e5%a4%87%e5%9f%ba%e7%a1%80","status":"publish","type":"post","link":"https:\/\/lttt.vanabel.cn\/?p=3615","title":{"rendered":"\u4e71\u8c08Peter Walters\u300aAn introduction to Ergodic Theory\u300b\u5fc5\u5907\u57fa\u7840"},"content":{"rendered":"<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u6211\u60f3\u8fd9\u91cc\u4e3b\u8981\u4ecb\u7ecd\u7684\u65f6Peter Walters\u7684\u4e66\u300aAn introduction to Ergodic Theory\u300b\uff0c\u5bf9\u4ed6\u672c\u4eba\u611f\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u53c2\u89c1\u4ed6\u7684<a href=\"http:\/\/www2.warwick.ac.uk\/fac\/sci\/maths\/people\/staff\/peter_walters\/\">\u4e3b\u9875<\/a>\u3002\u6211\u4e2a\u4eba\u8ba4\u4e3a\u5c31\u8457\u4e66\u98ce\u683c\u800c\u8a00\uff0c\u4e2d\u56fd\u79d1\u5927\u7684\u5f90\u68ee\u6797\u6559\u6388\u6bd4\u8f83\u63a5\u8fd1Peter Walters.<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u6211\u8eab\u8fb9\u6709\u4e9b\u4eba\u89c9\u5f97\u8fd9\u672c\u4e66\u4e0d\u592a\u597d\u8bfb\uff0c\u6709\u51e0\u4e2a\u4eba\u751a\u81f3\u534a\u9014\u800c\u5e9f\u3002\u5206\u6790\u5176\u4e3b\u8981\u539f\u56e0\u53ef\u80fd\u5c31\u662f\u7f3a\u4e4f\u4e00\u5b9a\u91cf\u7684\u6570\u5b66\u57fa\u7840\u77e5\u8bc6\u5bfc\u81f4\u3002\u8fd9\u672c\u4e66\u6240\u9700\u8981\u7684\u4e00\u4e9b\u6570\u5b66\u57fa\u7840\u5fc5\u5907\u77e5\u8bc6\u7f57\u5217\u5982\u4e0b\uff1a<br \/>\n<!--more--><br \/>\n1\uff1a\u76f8\u5bf9\u6df1\u539a\u7684\u6d4b\u5ea6\u8bba\u57fa\u7840\uff0c\u5bf9\u4e8e $\\pi $ \u7cfb, $\\lambda$ \u7cfb\uff0c\u5355\u8c03\u7c7b\u5b9a\u7406\u53ef\u4ee5\u719f\u7ec3\u5e94\u7528\uff0c\u5e94\u8be5\u8bf4\u8fd9\u662f\u6d4b\u5ea6\u8bba\u4e2d\u6700\u4e3a\u57fa\u672c\u7684\u77e5\u8bc6\u3002\u5bf9\u4e8e\u5176\u540e\u9a8c\u8bc1\u67d0\u4e2a\u5bf9\u5e94\u7684\u53d8\u6362\u662f\u5426\u4fdd\u6d4b\uff0c\u9700\u8981\u81f3\u5c11\u7075\u6d3b\u8fd9\u4e9b\u5185\u5bb9\uff0c\u5426\u5219\u5f53\u4f60\u5b66\u4e86\u4e00\u6bb5\u65f6\u95f4\u4e4b\u540e\uff0c\u4ecd\u7136\u65e0\u6cd5\u9a8c\u8bc1\u4e00\u4e2a\u6d4b\u5ea6\u7a7a\u95f4\u7684 two sided markov shift,one side shift \u7b49\u90fd\u662f\u4fdd\u6d4b\u53d8\u6362\u65f6\uff0c\u662f\u975e\u5e38\u6253\u51fb\u58eb\u6c14\u7684\u3002\u603b\u4e4b\u6d4b\u5ea6\u8bba\u662f\u8bfb\u8fd9\u672c\u4e66\u7684\u5fc5\u5907\u57fa\u7840\u3002\u5bf9\u4e8e\u8fd9\u4e00\u70b9\u4e0d\u751a\u719f\u6089\u7684\u8bfb\u8005\uff0c\u53ef\u4ee5\u53c2\u9605\u4e25\u4e16\u5efa\u548c\u5218\u79c0\u82b3\u7f16\u8457\u7684\u300a\u6d4b\u5ea6\u4e0e\u6982\u7387\u300b\u4e00\u4e66\uff0c\u91cc\u9762\u51e0\u4e4e\u6709\u4e86 Peter Walters \u4e66\u91cc\u5168\u90e8\u7684\u6d4b\u5ea6\u8bba\u5fc5\u5907\u57fa\u7840\u3002\u5e76\u4e14\u4e25\u5218\u4e66\u4e2d\u7684\u5f88\u591a\u8bc1\u660e\u5320\u5fc3\u72ec\u5177\uff0c\u5f88\u6709\u542f\u53d1\u6027\u3002\u6ca1\u6709\u6d89\u53ca\u5230\u7684\u77e5\u8bc6\u6050\u6015\u4e5f\u5c31\u662f\u4e00\u4e9b\u7c7b\u4f3c Lebesgue space\uff0cBoral space \u7684\u4e1c\u897f\uff0c\u4e0d\u8fc7\u8fd9\u4e9b\u5728 Peter Walters \u7684\u4e66\u91cc\u4e5f\u662f\u4e00\u5e26\u800c\u8fc7\uff0c\u6211\u6bd4\u8f83\u611f\u5174\u8da3\u7684\u4e00\u4e2a\u5c31\u662f\u5176\u4e2d\u4e00\u4e2a\u795e\u4f3c $C[0,1]$ \u4e07\u6709\u5b9a\u7406\u7684\u5e73\u884c\u7684\u6d4b\u5ea6\u8bba\u4e2d\u7684\u4e00\u4e2a\u7ed3\u679c\u3002<br \/>\n&nbsp;<br \/>\n2\uff1a\u76f8\u5bf9\u6df1\u539a\u7684\u6cdb\u51fd\u5206\u6790\uff08\u5f31\u62d3\u6251\uff0c\u5f31${}^\\ast$ \u62d3\u6251\uff09\u57fa\u7840\uff0c\u867d\u7136\u8fd9\u91cc\u8bb2\u7684\u662f\u6cdb\u51fd\u5206\u6790\u57fa\u7840\uff0c\u4f46\u662f\u6587\u4e2d\u771f\u6b63\u8981\u7d27\u7684\u662f\u5f31\u62d3\u6251\u57fa\u7840\uff0c\u548c\u5f31${}^\\ast$ \u62d3\u6251\u57fa\u7840\uff0c\u56e0\u4e3a\u5f53\u4f60\u8003\u8651\u628a Ergodic Theory \u8fd0\u7528\u5230\u62d3\u6251\u52a8\u529b\u7cfb\u7edf $(X,T)$ ($X$ \u4e3a\u7d27\u81f4\u7a7a\u95f4\uff0c$T$ \u4e3a\u8fde\u7eed\u6620\u5c04\uff0c\u76ee\u524d\u5927\u90e8\u5206\u7406\u8bba\u90fd\u662f\u5904\u7406\u7d27\u81f4\u7a7a\u95f4\u7684\u7406\u8bba\uff0cPeter Walters \u7684\u4e66\u4e2d\u5168\u90e8\u8ba8\u8bba\u7684\u90fd\u662f\u7d27\u81f4\u7a7a\u95f4\uff0c\u975e\u7d27\u7a7a\u95f4\u7684\u7406\u8bba\u6781\u5c11\uff09\uff0c\u8fd9\u5c31\u81ea\u7136\u9700\u8981\u4e0d\u53d8\u6d4b\u5ea6\u7684\u5f15\u8fdb\uff0c\u5f31${}^\\ast$ \u62d3\u6251\u4e0b\u7684\u8bf1\u5bfc\u7b97\u5b50\u5f31${}^\\ast$ \u62d3\u6251\u4e0b\u7684\u7d27\u6027\uff0c\u4f7f\u5f97 Schauder \u4e0d\u52a8\u70b9\u7684\u8fd0\u7528\u987a\u7406\u6210\u7ae0\u3002\u4f46\u662f\u73b0\u9636\u6bb5\u53ef\u80fd\u5f88\u5c11\u672c\u79d1\u751f\u7684\u6cdb\u51fd\u5206\u6790\u4f1a\u6d89\u53ca\u5f31\u62d3\u6251\u548c\u5f31${}^\\ast$ \u62d3\u6251\uff0c\u5e76\u4e14\u4e2d\u56fd\u5f0f\u7684\u6cdb\u51fd\u6559\u6750\u91cc\u9762\u8ba8\u8bba\u7684\u5f80\u5f80\u662f\u5f31\u6536\u655b\u548c\u5f31${}^\\ast$ \u6536\u655b\uff08\u5e8f\u5217\u610f\u4e49\u4e0b\uff09\uff0c\u800c\u4e00\u822c\u62d3\u6251\u672a\u5fc5\u80fd\u7528\u5e8f\u5217\u523b\u753b\u3002\u800c\u6211\u4eec\u592a\u591a\u7684\u6559\u6750\u505c\u7559\u5728\u4e3e\u4f8b\u5b50\u7684\u5c42\u6b21\u6765\u8bf4\u660e\u4e24\u79cd\u5b9a\u4e49\u7684\u5f3a\u5f31\uff0c\u5bfc\u81f4\u5f88\u591a\u4e2d\u6587\u4e13\u8457\u5728\u53d9\u8ff0\u5f31\u62d3\u6251\u65f6\u5019\u90fd\u72af\u5f88\u4e25\u91cd\u7684\u5931\u8bef\u3002\u8fd9\u65b9\u9762\u771f\u6b63\u6709\u89c1\u5730\u7684\u8bb2\u8ff0\u53ef\u53c2\u8003  Conway \u7684\u6cdb\u51fd\u5206\u6790\u91cc\u9762\u5f31\u62d3\u6251\u7684\u7ae0\u8282\u3002<br \/>\n&nbsp;<br \/>\n\u9700\u8981\u6307\u660e\u4e00\u70b9\u7684\u5c31\u662f Conway \u4e66\u4e2d\u5173\u4e8e\u5f31\u62d3\u6251\u5373 Peter Walters \u4e66\u4e2d\u7684\u5f31${}^\\ast$ \u62d3\u6251\uff0c\u8fd9\u662f\u4e00\u4e2a\u5f88\u6709\u610f\u601d\u7684\u73b0\u8c61\uff0c\u4ece\u4e8b\u6982\u7387\u8bba\u7684\u4eba\u559c\u6b22\u79f0\u5bf9\u5e94\u7684\u4e3a\u5f31\u6536\u655b\uff0c\u800c\u57fa\u672c\u4e0a\u5f88\u591a\u904d\u5386\u8bba\u7684\u4e66\u559c\u6b22\u79f0\u5176\u4e3a\u5f31${}^\\ast$ \u6536\u655b\uff0c\u5f53\u7136\u521d\u5b66\u7684\u65f6\u5019\u53ef\u80fd\u4f1a\u5929\u771f\u7684\u8ba4\u4e3a\u5c5e\u4e8e\u4f5c\u8005\u7684\u7528\u8bcd\u4e60\u60ef\u95ee\u9898\uff0c\u4f46\u662f\u9700\u8981\u6307\u660e\u7684\u662f\u8fd9\u4e24\u79cd\u7528\u6cd5\u5176\u5b9e\u90fd\u5bf9\uff0c\u66f4\u6df1\u7684\u5c42\u6b21\u662f\u683c\u7f57\u6ed5\u8fea\u514b50\u5e74\u4ee3\u7684\u4e00\u4e2a\u6cdb\u51fd\u5206\u6790\u7684\u7ed3\u679c\uff0c$(l^{ \\infty}) ^{*}$ \u4e0a\u7684\u5f31\u62d3\u6251\u548c\u5f31${}^\\ast$ \u62d3\u6251\u7b49\u4ef7\u3002\u5f53\u7136\u60f3\u77e5\u9053 $l^{ \\infty }$ \u5bf9\u5076\u7a7a\u95f4\u662f\u4ec0\u4e48\uff0c\u636e\u6211\u6240\u77e5\u4e2d\u6587\u7684\u4e66\u91cc\u9762\u597d\u50cf\u76ee\u524d\u53ea\u770b\u5230\u4e25\u52a0\u5b89\u5148\u751f\u7684\u6d4b\u5ea6\u8bba\u8bb2\u4e49\u4e2d\u8ba8\u8bba\u8fd9\u4e2a\u95ee\u9898\u3002<br \/>\n&nbsp;<br \/>\n3\uff1a\u7279\u5f81\u6807\u7406\u8bba\u548c\u7fa4\u4e0a\u7684\u8c03\u548c\u5206\u6790\u521d\u6b65<br \/>\n\u53ea\u8981\u7565\u5fae\u5b66\u8fc7\u4e9b\u7d27\u7fa4\u7684\u8868\u793a\u8bba\u4f1a\u6709\u5f88\u5927\u5e2e\u52a9\uff0c\u5c24\u5176\u662f\u5f53\u8ba8\u8bba\u5728\u67d0\u4e9b\u5c40\u90e8\u7d27\u7684\u53ef\u5ea6\u91cf\u7684\u7fa4\u4e0a\u7684\u904d\u5386\uff0cweak mixing\uff0cstrong mixing\u65f6\uff0c\u7279\u5f81\u6807\u7406\u8bba+\u8c31\u7406\u8bba\u8fd9\u4e24\u4e2a\u5de5\u5177\u5728\u904d\u5386\u8bba\u7684\u7ed3\u5408\u771f\u7684\u662f\u975e\u5e38\u6709\u610f\u601d\uff0c\u5f53\u7136\u8fd9\u4e00\u90e8\u5206\u57fa\u7840\u4e00\u822c\u53ef\u4ee5\u5728\u7fa4\u4e0a\u7684\u8c03\u548c\u5206\u6790\u4e2d\u83b7\u5f97\uff0c\u4f8b\u5982 Deitmar \u7684\u8c03\u548c\u5206\u6790<br \/>\n&nbsp;<br \/>\n4\uff1apositive matrix and non-negative matrix<br \/>\n\u77e9\u9635\u7684\u6027\u8d28\uff0c\u5c06\u4f1a\u5f71\u54cd symbolic system \u7684\u52a8\u529b\u5b66\u6027\u8d28\uff0c\u9887\u4e3a\u6709\u8da3\uff0c\u8fd9\u4e00\u90e8\u5206\u4e00\u822c\u4f1a\u5728\u77e9\u9635\u5206\u6790\u4e2d\u770b\u5230\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u6211\u60f3\u8fd9\u91cc\u4e3b\u8981\u4ecb\u7ecd\u7684\u65f6Peter Walters\u7684\u4e66\u300aAn int &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/lttt.vanabel.cn\/?p=3615\"> <span class=\"screen-reader-text\">\u4e71\u8c08Peter Walters\u300aAn introduction to Ergodic Theory\u300b\u5fc5\u5907\u57fa\u7840<\/span> \u9605\u8bfb\u66f4\u591a &raquo;<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[365,372,168],"class_list":["post-3615","post","type-post","status-publish","format-standard","hentry","category-mathnotes","tag-dynamic-system","tag-ergodic-theory","tag-ast-"],"_links":{"self":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/3615","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3615"}],"version-history":[{"count":0,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/3615\/revisions"}],"wp:attachment":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3615"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3615"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3615"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}