. . . . . . . "Center manifold"@en . . . . . "1106880670"^^ . . . . . . . . "In the mathematics of evolving systems, the concept of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised to be fundamental to mathematical modelling. Center manifolds play an important role in bifurcation theory because interesting behavior takes place on the center manifold and in multiscale mathematics because the long time dynamics of the micro-scale often are attracted to a relatively simple center manifold involving the coarse scale variables."@en . . . "\u0426\u0435\u043D\u0442\u0440\u0430\u0301\u043B\u044C\u043D\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0301\u0437\u0438\u0435 \u043E\u0441\u043E\u0431\u043E\u0439 \u0442\u043E\u0447\u043A\u0438 \u0430\u0432\u0442\u043E\u043D\u043E\u043C\u043D\u043E\u0433\u043E \u043E\u0431\u044B\u043A\u043D\u043E\u0432\u0435\u043D\u043D\u043E\u0433\u043E \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u2014 \u0438\u043D\u0432\u0430\u0440\u0438\u0430\u043D\u0442\u043D\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435 \u0432 \u0444\u0430\u0437\u043E\u0432\u043E\u043C \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0435, \u043F\u0440\u043E\u0445\u043E\u0434\u044F\u0449\u0435\u0435 \u0447\u0435\u0440\u0435\u0437 \u043E\u0441\u043E\u0431\u0443\u044E \u0442\u043E\u0447\u043A\u0443 \u0438 \u043A\u0430\u0441\u0430\u044E\u0449\u0435\u0435\u0441\u044F \u0438\u043D\u0432\u0430\u0440\u0438\u0430\u043D\u0442\u043D\u043E\u0433\u043E \u0446\u0435\u043D\u0442\u0440\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u043F\u043E\u0434\u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430 \u043B\u0438\u043D\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F. \u0412\u0430\u0436\u043D\u044B\u0439 \u043E\u0431\u044A\u0435\u043A\u0442 \u0438\u0437\u0443\u0447\u0435\u043D\u0438\u044F \u0442\u0435\u043E\u0440\u0438\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0438 \u0434\u0438\u043D\u0430\u043C\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043C. \u0412 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0441\u043C\u044B\u0441\u043B\u0435, \u0432\u0441\u044F \u043D\u0435\u0442\u0440\u0438\u0432\u0438\u0430\u043B\u044C\u043D\u0430\u044F \u0434\u0438\u043D\u0430\u043C\u0438\u043A\u0430 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u0432 \u043E\u043A\u0440\u0435\u0441\u0442\u043D\u043E\u0441\u0442\u0438 \u043E\u0441\u043E\u0431\u043E\u0439 \u0442\u043E\u0447\u043A\u0438 \u0441\u043E\u0441\u0440\u0435\u0434\u043E\u0442\u043E\u0447\u0435\u043D\u0430 \u043D\u0430 \u0446\u0435\u043D\u0442\u0440\u0430\u043B\u044C\u043D\u043E\u043C \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0438."@ru . . . . . "3948656"^^ . . . . . . . . . . . "\u4E2D\u5FC3\u6D41\u5F62\uFF08center manifold\uFF09\u662F\u52D5\u529B\u7CFB\u7D71\u6578\u5B78\u7406\u8AD6\u7684\u4E00\u90E8\u4EFD\uFF0C\u6700\u65E9\u662F\u7528\u6B64\u6982\u5FF5\u4F86\u5224\u65B7\u9000\u5316\u5E73\u8861\u9EDE\u7684\u7A69\u5B9A\u6027\u3002\u4E4B\u5F8C\u9019\u500B\u6982\u5FF5\u6210\u70BA\u6570\u5B66\u6A21\u578B\u7684\u5EFA\u69CB\u57FA\u790E\u3002 \u82E5\u5C07\u7403\u5F80\u4E0A\u62CB\u3002\u53EF\u6839\u64DA\u725B\u987F\u8FD0\u52A8\u5B9A\u5F8B\u9810\u6E2C\u7403\u7684\u904B\u52D5\uFF0C\u65B9\u5F0F\u662F\u6C42\u89E3\u6709\u5176\u4F4D\u7F6E\u4EE5\u53CA\u901F\u5EA6\u7684\u5FAE\u5206\u65B9\u7A0B\uFF0C\u4F46\u5728\u6642\u7684\u884C\u70BA\u5C31\u7121\u6CD5\u7528\u725B\u987F\u8FD0\u52A8\u5B9A\u5F8B\u4F86\u63CF\u8FF0\u3002\u5728\u7403\u53CD\u5F48\u6642\uFF0C\u7403\u6703\u6709\u5F62\u8B8A\uFF0C\u5C31\u7121\u6CD5\u7528\u525B\u9AD4\u7684\u725B\u987F\u8FD0\u52A8\u5B9A\u5F8B\u4F86\u9810\u6E2C\u7CFB\u7D71\u7684\u6F14\u9032\uFF0C\u9700\u8981\u7528\u8FDE\u7EED\u4ECB\u8D28\u529B\u5B66\u4F86\u63CF\u8FF0\u7D44\u6210\u7403\u7684\u6240\u6709\u7C92\u5B50\u5728\u5F62\u8B8A\u524D\u5F8C\u7684\u884C\u70BA\u3002\u5728\u53CD\u5F48\u5F8C\uFF0C\u7403\u7684\u5F62\u8B8A\u6703\u5FEB\u901F\u6D88\u5931\uFF0C\u7403\u7E7C\u7E8C\u4F9D\u5FAA\u725B\u987F\u8FD0\u52A8\u5B9A\u5F8B\u3002\u82E5\u5C07\u7403\u8996\u70BA\u662F\u7531\u8A31\u591A\u4E92\u76F8\u5F71\u97FF\u7684\u6210\u4EFD\u6240\u7D44\u6210\u7684\u7CFB\u7D71\uFF0C\u725B\u9813\u904B\u52D5\u5B9A\u5F8B\u5C0D\u7403\u7684\u63CF\u8FF0\uFF0C\u53EA\u4EE5\u4F4D\u7F6E\u3001\u901F\u5EA6\u53CA\u65CB\u8F49\u65B9\u5F0F\u5448\u73FE\uFF0C\u5373\u70BA\u8B8A\u5F62\u7403\u7684\u4E2D\u5FC3\u6D41\u5F62\u3002\u82E5\u6709\u4E00\u7CFB\u7D71\u662F\u7531\u8A31\u591A\u4E92\u76F8\u5F71\u97FF\u6210\u4EFD\u6240\u7D44\u6210\uFF0C\u800C\u5176\u5F71\u97FF\u6548\u61C9\u6703\u5FEB\u901F\u8870\u6E1B\uFF0C\u53EF\u4EE5\u7528\u4E2D\u5FC3\u6D41\u5F62\uFF0C\u4EE5\u8F03\u7C21\u55AE\u7684\u65B9\u5F0F\u4F86\u63CF\u8FF0\u7CFB\u7D71\u3002 \u4E2D\u5FC3\u6D41\u5F62\u5728\u5206\u5C94\u7406\u8AD6\u4E2D\u6709\u91CD\u8981\u7684\u5730\u4F4D\uFF0C\u56E0\u70BA\u7CFB\u7D71\u5728\u4E2D\u5FC3\u6D41\u5F62\u7684\u4F4D\u7F6E\u6703\u51FA\u73FE\u7279\u6B8A\u7684\u884C\u70BA\uFF0C\u5728\u4E2D\u4E5F\u5F88\u91CD\u8981\uFF0C\u5FAE\u5C3A\u5EA6\u7684\u9577\u6642\u9593\u52D5\u614B\u5E38\u5E38\u6703\u53D7\u5230\u76F8\u5C0D\u7C21\u55AE\u3001\u8B8A\u6578\u5C3A\u5EA6\u8F03\u5927\u7684\u4E2D\u5FC3\u6D41\u5F62\u5438\u5F15\u3002"@zh . "\u4E2D\u5FC3\u6D41\u5F62\uFF08center manifold\uFF09\u662F\u52D5\u529B\u7CFB\u7D71\u6578\u5B78\u7406\u8AD6\u7684\u4E00\u90E8\u4EFD\uFF0C\u6700\u65E9\u662F\u7528\u6B64\u6982\u5FF5\u4F86\u5224\u65B7\u9000\u5316\u5E73\u8861\u9EDE\u7684\u7A69\u5B9A\u6027\u3002\u4E4B\u5F8C\u9019\u500B\u6982\u5FF5\u6210\u70BA\u6570\u5B66\u6A21\u578B\u7684\u5EFA\u69CB\u57FA\u790E\u3002 \u82E5\u5C07\u7403\u5F80\u4E0A\u62CB\u3002\u53EF\u6839\u64DA\u725B\u987F\u8FD0\u52A8\u5B9A\u5F8B\u9810\u6E2C\u7403\u7684\u904B\u52D5\uFF0C\u65B9\u5F0F\u662F\u6C42\u89E3\u6709\u5176\u4F4D\u7F6E\u4EE5\u53CA\u901F\u5EA6\u7684\u5FAE\u5206\u65B9\u7A0B\uFF0C\u4F46\u5728\u6642\u7684\u884C\u70BA\u5C31\u7121\u6CD5\u7528\u725B\u987F\u8FD0\u52A8\u5B9A\u5F8B\u4F86\u63CF\u8FF0\u3002\u5728\u7403\u53CD\u5F48\u6642\uFF0C\u7403\u6703\u6709\u5F62\u8B8A\uFF0C\u5C31\u7121\u6CD5\u7528\u525B\u9AD4\u7684\u725B\u987F\u8FD0\u52A8\u5B9A\u5F8B\u4F86\u9810\u6E2C\u7CFB\u7D71\u7684\u6F14\u9032\uFF0C\u9700\u8981\u7528\u8FDE\u7EED\u4ECB\u8D28\u529B\u5B66\u4F86\u63CF\u8FF0\u7D44\u6210\u7403\u7684\u6240\u6709\u7C92\u5B50\u5728\u5F62\u8B8A\u524D\u5F8C\u7684\u884C\u70BA\u3002\u5728\u53CD\u5F48\u5F8C\uFF0C\u7403\u7684\u5F62\u8B8A\u6703\u5FEB\u901F\u6D88\u5931\uFF0C\u7403\u7E7C\u7E8C\u4F9D\u5FAA\u725B\u987F\u8FD0\u52A8\u5B9A\u5F8B\u3002\u82E5\u5C07\u7403\u8996\u70BA\u662F\u7531\u8A31\u591A\u4E92\u76F8\u5F71\u97FF\u7684\u6210\u4EFD\u6240\u7D44\u6210\u7684\u7CFB\u7D71\uFF0C\u725B\u9813\u904B\u52D5\u5B9A\u5F8B\u5C0D\u7403\u7684\u63CF\u8FF0\uFF0C\u53EA\u4EE5\u4F4D\u7F6E\u3001\u901F\u5EA6\u53CA\u65CB\u8F49\u65B9\u5F0F\u5448\u73FE\uFF0C\u5373\u70BA\u8B8A\u5F62\u7403\u7684\u4E2D\u5FC3\u6D41\u5F62\u3002\u82E5\u6709\u4E00\u7CFB\u7D71\u662F\u7531\u8A31\u591A\u4E92\u76F8\u5F71\u97FF\u6210\u4EFD\u6240\u7D44\u6210\uFF0C\u800C\u5176\u5F71\u97FF\u6548\u61C9\u6703\u5FEB\u901F\u8870\u6E1B\uFF0C\u53EF\u4EE5\u7528\u4E2D\u5FC3\u6D41\u5F62\uFF0C\u4EE5\u8F03\u7C21\u55AE\u7684\u65B9\u5F0F\u4F86\u63CF\u8FF0\u7CFB\u7D71\u3002 \u4E2D\u5FC3\u6D41\u5F62\u5728\u5206\u5C94\u7406\u8AD6\u4E2D\u6709\u91CD\u8981\u7684\u5730\u4F4D\uFF0C\u56E0\u70BA\u7CFB\u7D71\u5728\u4E2D\u5FC3\u6D41\u5F62\u7684\u4F4D\u7F6E\u6703\u51FA\u73FE\u7279\u6B8A\u7684\u884C\u70BA\uFF0C\u5728\u4E2D\u4E5F\u5F88\u91CD\u8981\uFF0C\u5FAE\u5C3A\u5EA6\u7684\u9577\u6642\u9593\u52D5\u614B\u5E38\u5E38\u6703\u53D7\u5230\u76F8\u5C0D\u7C21\u55AE\u3001\u8B8A\u6578\u5C3A\u5EA6\u8F03\u5927\u7684\u4E2D\u5FC3\u6D41\u5F62\u5438\u5F15\u3002"@zh . . "\u0426\u0435\u043D\u0442\u0440\u0430\u0301\u043B\u044C\u043D\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0301\u0437\u0438\u0435 \u043E\u0441\u043E\u0431\u043E\u0439 \u0442\u043E\u0447\u043A\u0438 \u0430\u0432\u0442\u043E\u043D\u043E\u043C\u043D\u043E\u0433\u043E \u043E\u0431\u044B\u043A\u043D\u043E\u0432\u0435\u043D\u043D\u043E\u0433\u043E \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u2014 \u0438\u043D\u0432\u0430\u0440\u0438\u0430\u043D\u0442\u043D\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435 \u0432 \u0444\u0430\u0437\u043E\u0432\u043E\u043C \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0435, \u043F\u0440\u043E\u0445\u043E\u0434\u044F\u0449\u0435\u0435 \u0447\u0435\u0440\u0435\u0437 \u043E\u0441\u043E\u0431\u0443\u044E \u0442\u043E\u0447\u043A\u0443 \u0438 \u043A\u0430\u0441\u0430\u044E\u0449\u0435\u0435\u0441\u044F \u0438\u043D\u0432\u0430\u0440\u0438\u0430\u043D\u0442\u043D\u043E\u0433\u043E \u0446\u0435\u043D\u0442\u0440\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u043F\u043E\u0434\u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430 \u043B\u0438\u043D\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F. \u0412\u0430\u0436\u043D\u044B\u0439 \u043E\u0431\u044A\u0435\u043A\u0442 \u0438\u0437\u0443\u0447\u0435\u043D\u0438\u044F \u0442\u0435\u043E\u0440\u0438\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0438 \u0434\u0438\u043D\u0430\u043C\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043C. \u0412 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0441\u043C\u044B\u0441\u043B\u0435, \u0432\u0441\u044F \u043D\u0435\u0442\u0440\u0438\u0432\u0438\u0430\u043B\u044C\u043D\u0430\u044F \u0434\u0438\u043D\u0430\u043C\u0438\u043A\u0430 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u0432 \u043E\u043A\u0440\u0435\u0441\u0442\u043D\u043E\u0441\u0442\u0438 \u043E\u0441\u043E\u0431\u043E\u0439 \u0442\u043E\u0447\u043A\u0438 \u0441\u043E\u0441\u0440\u0435\u0434\u043E\u0442\u043E\u0447\u0435\u043D\u0430 \u043D\u0430 \u0446\u0435\u043D\u0442\u0440\u0430\u043B\u044C\u043D\u043E\u043C \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0438."@ru . "Variet\u00E0 centrale"@it . . . "In matematica, in particolare nello studio dei sistemi dinamici, la variet\u00E0 centrale di un punto di equilibrio di un sistema dinamico consiste nelle orbite il cui comportamento in prossimit\u00E0 del punto di equilibrio non \u00E8 soggetto n\u00E9 all'attrazione della variet\u00E0 stabile n\u00E9 alla repulsione di quella instabile. Sia dato un sistema dinamico: dove \u00E8 una matrice costante, \u00E8 di classe con in un intorno del punto di equilibrio isolato e: Se e sono le variet\u00E0 stabile ed instabile dell'equazione: detto lo spazio generato dagli autovettori di associati ad autovalori con parte reale nulla, esiste una variet\u00E0 invariante , detta variet\u00E0 centrale, tangente in prossimit\u00E0 del punto di equilibrio. Non \u00E8 necessariamente unica."@it . . "\u4E2D\u5FC3\u6D41\u5F62"@zh . . . . . . . . . . "center_manifold"@en . . . . . "In the mathematics of evolving systems, the concept of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised to be fundamental to mathematical modelling. Center manifolds play an important role in bifurcation theory because interesting behavior takes place on the center manifold and in multiscale mathematics because the long time dynamics of the micro-scale often are attracted to a relatively simple center manifold involving the coarse scale variables."@en . "\u0426\u0435\u043D\u0442\u0440\u0430\u043B\u044C\u043D\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435"@ru . . . . . . . "In matematica, in particolare nello studio dei sistemi dinamici, la variet\u00E0 centrale di un punto di equilibrio di un sistema dinamico consiste nelle orbite il cui comportamento in prossimit\u00E0 del punto di equilibrio non \u00E8 soggetto n\u00E9 all'attrazione della variet\u00E0 stabile n\u00E9 alla repulsione di quella instabile. Sia dato un sistema dinamico: dove \u00E8 una matrice costante, \u00E8 di classe con in un intorno del punto di equilibrio isolato e: Se e sono le variet\u00E0 stabile ed instabile dell'equazione:"@it . . . . . . "Jack Carr"@en . . . . . . "20797"^^ . . "Center manifold"@en . . .