. "Th\u00E9or\u00E8me de Hartman-Grobman"@fr . . . . . . . . . . . "Twierdzenie Hartmana-Grobmana"@pl . . "En math\u00E9matiques, dans l'\u00E9tude des syst\u00E8mes dynamiques, le th\u00E9or\u00E8me de Hartman-Grobman ou th\u00E9or\u00E8me de lin\u00E9arisation est un th\u00E9or\u00E8me important concernant le comportement local des syst\u00E8mes dynamiques au voisinage d'un (en). Essentiellement, ce th\u00E9or\u00E8me \u00E9nonce qu'un syst\u00E8me dynamique, au voisinage d'un \u00E9quilibre hyperbolique, se comporte qualitativement de la m\u00EAme mani\u00E8re que le syst\u00E8me lin\u00E9aris\u00E9 au voisinage de l'origine. Par cons\u00E9quent, lorsque l'on est en pr\u00E9sence d'un tel syst\u00E8me, on utilise plut\u00F4t la lin\u00E9arisation, plus facile \u00E0 analyser, pour \u00E9tudier son comportement."@fr . . . . "In mathematics, in the study of dynamical systems, the Hartman\u2013Grobman theorem or linearisation theorem is a theorem about the local behaviour of dynamical systems in the neighbourhood of a hyperbolic equilibrium point. It asserts that linearisation\u2014a natural simplification of the system\u2014is effective in predicting qualitative patterns of behaviour. The theorem owes its name to Philip Hartman and ."@en . . . . . "\u529B\u5B66\u7CFB\u306E\u7406\u8AD6\u306B\u304A\u3044\u3066\u3001\u30CF\u30FC\u30C8\u30DE\u30F3\uFF1D\u30B0\u30ED\u30D6\u30DE\u30F3\u306E\u5B9A\u7406(\u82F1: Hartman\u2013Grobman theorem)\u3068\u306F\u3001\u4E0D\u52D5\u70B9\u5468\u308A\u306E\u89E3\u6790\u306B\u304A\u3044\u3066\u3001\u5143\u306E\u65B9\u7A0B\u5F0F\u3068\u8FD1\u4F3C\u7684\u306B\u7DDA\u5F62\u5316\u3057\u305F\u65B9\u7A0B\u5F0F\u304C\u5C40\u6240\u7684\u306B\u7B49\u4FA1\u3067\u3042\u308B\u3053\u3068\u3092\u793A\u3059\u5B9A\u7406\u3002\u6570\u5B66\u8005D. M. \u30B0\u30ED\u30D6\u30DE\u30F3\u3068P. \u30CF\u30FC\u30C8\u30DE\u30F3\u306B\u3088\u3063\u3066\u793A\u3055\u308C\u305F\u3002"@ja . . "Teorema de Hartman\u2013Grobman"@ca . . "Hartman\u2013Grobman theorem"@en . . . "\u529B\u5B66\u7CFB\u306E\u7406\u8AD6\u306B\u304A\u3044\u3066\u3001\u30CF\u30FC\u30C8\u30DE\u30F3\uFF1D\u30B0\u30ED\u30D6\u30DE\u30F3\u306E\u5B9A\u7406(\u82F1: Hartman\u2013Grobman theorem)\u3068\u306F\u3001\u4E0D\u52D5\u70B9\u5468\u308A\u306E\u89E3\u6790\u306B\u304A\u3044\u3066\u3001\u5143\u306E\u65B9\u7A0B\u5F0F\u3068\u8FD1\u4F3C\u7684\u306B\u7DDA\u5F62\u5316\u3057\u305F\u65B9\u7A0B\u5F0F\u304C\u5C40\u6240\u7684\u306B\u7B49\u4FA1\u3067\u3042\u308B\u3053\u3068\u3092\u793A\u3059\u5B9A\u7406\u3002\u6570\u5B66\u8005D. M. \u30B0\u30ED\u30D6\u30DE\u30F3\u3068P. \u30CF\u30FC\u30C8\u30DE\u30F3\u306B\u3088\u3063\u3066\u793A\u3055\u308C\u305F\u3002"@ja . . . . . . "In matematica, in particolare nello studio dei sistemi dinamici, il teorema di Hartman-Grobman o teorema di linearizzazione \u00E8 un importante teorema che descrive il comportamento di un sistema dinamico nell'intorno di un punto di equilibrio iperbolico. Fondamentalmente il teorema afferma che il comportamento di un sistema dinamico nei pressi di un punto di equilibrio iperbolico \u00E8 qualitativamente simile a quello della sua linearizzazione intorno a quel punto. Quindi utilizzando la sua linearizzazione se ne possono studiare pi\u00F9 agevolmente alcune caratteristiche."@it . "\u30CF\u30FC\u30C8\u30DE\u30F3\uFF1D\u30B0\u30ED\u30D6\u30DE\u30F3\u306E\u5B9A\u7406"@ja . "Twierdzenie Hartmana-Grobmana \u2013 twierdzenie jako\u015Bciowej teorii r\u00F3wna\u0144 r\u00F3\u017Cniczkowych zwyczajnych m\u00F3wi\u0105ce, \u017Ce je\u015Bli macierz linearyzacji r\u00F3wnania nie ma czysto urojonych warto\u015Bci w\u0142asnych, to r\u00F3wnanie jest topologicznie sprz\u0119\u017Cone ze swoj\u0105 linearyzacj\u0105."@pl . . . . . . . "A matem\u00E0tiques, a l'estudi de sistemes din\u00E0mics, el teorema de Hartman-Grobman o el teorema de linelitzaci\u00F3 \u00E9s el teorema que tracta del comportament local del sistema al voltant d'un punt d'equilibri. B\u00E0sicament, el teorema anuncia que el comportament del sistema din\u00E0mic prop d'un punt d'equilibri \u00E9s qualitativament el mateix que el comportament que la seva linealitzaci\u00F3 prop del mateix punt d'equilibri si i nom\u00E9s si tots els valors propis de la linealitzaci\u00F3 tenen part real diferent de zero."@ca . . . . . "En math\u00E9matiques, dans l'\u00E9tude des syst\u00E8mes dynamiques, le th\u00E9or\u00E8me de Hartman-Grobman ou th\u00E9or\u00E8me de lin\u00E9arisation est un th\u00E9or\u00E8me important concernant le comportement local des syst\u00E8mes dynamiques au voisinage d'un (en). Essentiellement, ce th\u00E9or\u00E8me \u00E9nonce qu'un syst\u00E8me dynamique, au voisinage d'un \u00E9quilibre hyperbolique, se comporte qualitativement de la m\u00EAme mani\u00E8re que le syst\u00E8me lin\u00E9aris\u00E9 au voisinage de l'origine. Par cons\u00E9quent, lorsque l'on est en pr\u00E9sence d'un tel syst\u00E8me, on utilise plut\u00F4t la lin\u00E9arisation, plus facile \u00E0 analyser, pour \u00E9tudier son comportement."@fr . . "\u0645\u0628\u0631\u0647\u0646\u0629 \u0647\u0627\u0631\u062A\u0645\u0627\u0646-\u063A\u0631\u0648\u0628\u0645\u0627\u0646"@ar . "Der Satz von Hartman-Grobman, auch bekannt als Linearisierungssatz, besagt, dass das Verhalten eines dynamischen Systems in Form eines Autonomen Differentialgleichungssystems in der Umgebung eines hyperbolischen Fixpunkts dem Verhalten des um diesen Punkt linearisierten Systems gleicht. Hyperbolischer Fixpunkt bedeutet, dass keiner der Eigenwerte des linearisierten Systems den Realteil Null hat. Benannt ist der Satz nach dem US-Amerikaner Philip Hartman und dem Russen , die den Satz unabh\u00E4ngig voneinander 1960 bzw. 1959 ver\u00F6ffentlichten. Nach dem Satz kann man in der Umgebung eines solchen Fixpunkts also lokal das Verhalten eines nichtlinearen Systems aus dem der linearisierten Gleichungen erschlie\u00DFen."@de . . . . . "In mathematics, in the study of dynamical systems, the Hartman\u2013Grobman theorem or linearisation theorem is a theorem about the local behaviour of dynamical systems in the neighbourhood of a hyperbolic equilibrium point. It asserts that linearisation\u2014a natural simplification of the system\u2014is effective in predicting qualitative patterns of behaviour. The theorem owes its name to Philip Hartman and . The theorem states that the behaviour of a dynamical system in a domain near a hyperbolic equilibrium point is qualitatively the same as the behaviour of its linearisation near this equilibrium point, where hyperbolicity means that no eigenvalue of the linearisation has real part equal to zero. Therefore, when dealing with such dynamical systems one can use the simpler linearisation of the system to analyse its behaviour around equilibria."@en . . . "\u062A\u0642\u0648\u0644 \u0645\u0628\u0631\u0647\u0646\u0629 \u0647\u0627\u0631\u062A\u0645\u0627\u0646-\u063A\u0631\u0648\u0628\u0645\u0627\u0646 Hartman-Grobman (\u0627\u0644\u062A\u064A \u062A\u0633\u0645\u0649 \u0623\u064A\u0636\u0627\u064B \u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0625\u062E\u0637\u0627\u0637 \u0623\u0648 \u0627\u0644\u0627\u0633\u062A\u062E\u0637\u0627\u0637) \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646\u062A \u0646\u0642\u0637\u0629 \u0633\u0643\u0648\u0646 \u0646\u0638\u0627\u0645 \u0645\u0627 \u0641\u0625\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0638\u0627\u0645 \u0645\u0637\u0627\u0628\u0642 \u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0627 \u0644\u062A\u062E\u0637\u064A\u0637\u0647 \u0639\u0646\u062F \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629. \u0623\u064A \u0623\u0646 \u062D\u0644 \u0627\u0644\u0645\u0639\u0627\u062F\u0644\u0629 \u0627\u0644\u062A\u0641\u0627\u0636\u0644\u064A\u0629 \u0627\u0644\u0623\u0635\u0644\u064A\u0629 \u0648\u062D\u0644 \u0627\u0644\u0645\u0639\u0627\u062F\u0644\u0629 \u0627\u0644\u062A\u0641\u0627\u0636\u0644\u064A\u0629 \u0627\u0644\u0645\u062E\u0637\u0637\u0629 \u0627\u0644\u062A\u0627\u0628\u0639\u0629 \u0644\u0647\u0627 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0633\u0644\u0648\u0643 \u0641\u064A \u0645\u062D\u064A\u0637 \u0646\u0642\u0637\u0629 \u0633\u0643\u0648\u0646 \u0625\u0647\u0644\u064A\u062C\u064A\u0629. \u0648\u0645\u0639\u0646\u0649 \u0646\u0642\u0637\u0629 \u0633\u0643\u0648\u0646 \u0625\u0647\u0644\u064A\u062C\u064A\u0629 \u0647\u0648 \u0623\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0646\u0627\u062A\u062C\u0629 \u0639\u0646 \u062A\u062E\u0637\u064A\u0637 \u0627\u0644\u0646\u0638\u0627\u0645 \u0639\u0646\u062F \u0646\u0642\u0637\u0629 \u0627\u0644\u0633\u0643\u0648\u0646 \u0644\u0627 \u062A\u062D\u062A\u0648\u064A \u0639\u0644\u0649 \u0642\u064A\u0645 \u0630\u0627\u062A\u064A\u0629 \u064A\u0643\u0648\u0646 \u0627\u0644\u062C\u0632\u0621 \u0627\u0644\u062D\u0642\u064A\u0642\u064A \u0645\u0646\u0647\u0627 \u0635\u0641\u0631\u0627."@ar . "Der Satz von Hartman-Grobman, auch bekannt als Linearisierungssatz, besagt, dass das Verhalten eines dynamischen Systems in Form eines Autonomen Differentialgleichungssystems in der Umgebung eines hyperbolischen Fixpunkts dem Verhalten des um diesen Punkt linearisierten Systems gleicht. Hyperbolischer Fixpunkt bedeutet, dass keiner der Eigenwerte des linearisierten Systems den Realteil Null hat. Benannt ist der Satz nach dem US-Amerikaner Philip Hartman und dem Russen , die den Satz unabh\u00E4ngig voneinander 1960 bzw. 1959 ver\u00F6ffentlichten."@de . "\u0412 \u0442\u0435\u043E\u0440\u0438\u0438 \u0434\u0438\u043D\u0430\u043C\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043C, \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0413\u0440\u043E\u0431\u043C\u0430\u043D\u0430 \u2014 \u0425\u0430\u0440\u0442\u043C\u0430\u043D\u0430 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442, \u0447\u0442\u043E \u0432 \u043E\u043A\u0440\u0435\u0441\u0442\u043D\u043E\u0441\u0442\u0438 \u0433\u0438\u043F\u0435\u0440\u0431\u043E\u043B\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u043D\u0435\u043F\u043E\u0434\u0432\u0438\u0436\u043D\u043E\u0439 \u0442\u043E\u0447\u043A\u0438 \u043F\u043E\u0432\u0435\u0434\u0435\u043D\u0438\u0435 \u0434\u0438\u043D\u0430\u043C\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u0441 \u0442\u043E\u0447\u043D\u043E\u0441\u0442\u044C\u044E \u0434\u043E \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u043E\u0439 \u0437\u0430\u043C\u0435\u043D\u044B \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442 \u0441\u043E\u0432\u043F\u0430\u0434\u0430\u0435\u0442 \u0441 \u043F\u043E\u0432\u0435\u0434\u0435\u043D\u0438\u0435\u043C \u0435\u0451 \u043B\u0438\u043D\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u0438. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0441\u043E\u0432\u0435\u0442\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0414. \u041C. \u0413\u0440\u043E\u0431\u043C\u0430\u043D\u0430 \u0438 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0424. \u0425\u0430\u0440\u0442\u043C\u0430\u043D\u0430, \u043F\u043E\u043B\u0443\u0447\u0438\u0432\u0448\u0438\u043C \u044D\u0442\u043E\u0442 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u043D\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043C\u043E \u0434\u0440\u0443\u0433 \u043E\u0442 \u0434\u0440\u0443\u0433\u0430."@ru . . . . "In matematica, in particolare nello studio dei sistemi dinamici, il teorema di Hartman-Grobman o teorema di linearizzazione \u00E8 un importante teorema che descrive il comportamento di un sistema dinamico nell'intorno di un punto di equilibrio iperbolico. Fondamentalmente il teorema afferma che il comportamento di un sistema dinamico nei pressi di un punto di equilibrio iperbolico \u00E8 qualitativamente simile a quello della sua linearizzazione intorno a quel punto. Quindi utilizzando la sua linearizzazione se ne possono studiare pi\u00F9 agevolmente alcune caratteristiche."@it . . "1068276148"^^ . . . "9071"^^ . . . "9933752"^^ . . "Teorema di Hartman-Grobman"@it . . "Twierdzenie Hartmana-Grobmana \u2013 twierdzenie jako\u015Bciowej teorii r\u00F3wna\u0144 r\u00F3\u017Cniczkowych zwyczajnych m\u00F3wi\u0105ce, \u017Ce je\u015Bli macierz linearyzacji r\u00F3wnania nie ma czysto urojonych warto\u015Bci w\u0142asnych, to r\u00F3wnanie jest topologicznie sprz\u0119\u017Cone ze swoj\u0105 linearyzacj\u0105."@pl . . "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u0413\u0440\u043E\u0431\u043C\u0430\u043D\u0430 \u2014 \u0425\u0430\u0440\u0442\u043C\u0430\u043D\u0430"@ru . . "\u0412 \u0442\u0435\u043E\u0440\u0438\u0438 \u0434\u0438\u043D\u0430\u043C\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043C, \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0413\u0440\u043E\u0431\u043C\u0430\u043D\u0430 \u2014 \u0425\u0430\u0440\u0442\u043C\u0430\u043D\u0430 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442, \u0447\u0442\u043E \u0432 \u043E\u043A\u0440\u0435\u0441\u0442\u043D\u043E\u0441\u0442\u0438 \u0433\u0438\u043F\u0435\u0440\u0431\u043E\u043B\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u043D\u0435\u043F\u043E\u0434\u0432\u0438\u0436\u043D\u043E\u0439 \u0442\u043E\u0447\u043A\u0438 \u043F\u043E\u0432\u0435\u0434\u0435\u043D\u0438\u0435 \u0434\u0438\u043D\u0430\u043C\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u0441 \u0442\u043E\u0447\u043D\u043E\u0441\u0442\u044C\u044E \u0434\u043E \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u043E\u0439 \u0437\u0430\u043C\u0435\u043D\u044B \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442 \u0441\u043E\u0432\u043F\u0430\u0434\u0430\u0435\u0442 \u0441 \u043F\u043E\u0432\u0435\u0434\u0435\u043D\u0438\u0435\u043C \u0435\u0451 \u043B\u0438\u043D\u0435\u0430\u0440\u0438\u0437\u0430\u0446\u0438\u0438. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0441\u043E\u0432\u0435\u0442\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0414. \u041C. \u0413\u0440\u043E\u0431\u043C\u0430\u043D\u0430 \u0438 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0424. \u0425\u0430\u0440\u0442\u043C\u0430\u043D\u0430, \u043F\u043E\u043B\u0443\u0447\u0438\u0432\u0448\u0438\u043C \u044D\u0442\u043E\u0442 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u043D\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043C\u043E \u0434\u0440\u0443\u0433 \u043E\u0442 \u0434\u0440\u0443\u0433\u0430."@ru . . . . . "\u062A\u0642\u0648\u0644 \u0645\u0628\u0631\u0647\u0646\u0629 \u0647\u0627\u0631\u062A\u0645\u0627\u0646-\u063A\u0631\u0648\u0628\u0645\u0627\u0646 Hartman-Grobman (\u0627\u0644\u062A\u064A \u062A\u0633\u0645\u0649 \u0623\u064A\u0636\u0627\u064B \u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0625\u062E\u0637\u0627\u0637 \u0623\u0648 \u0627\u0644\u0627\u0633\u062A\u062E\u0637\u0627\u0637) \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646\u062A \u0646\u0642\u0637\u0629 \u0633\u0643\u0648\u0646 \u0646\u0638\u0627\u0645 \u0645\u0627 \u0641\u0625\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0638\u0627\u0645 \u0645\u0637\u0627\u0628\u0642 \u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0627 \u0644\u062A\u062E\u0637\u064A\u0637\u0647 \u0639\u0646\u062F \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629. \u0623\u064A \u0623\u0646 \u062D\u0644 \u0627\u0644\u0645\u0639\u0627\u062F\u0644\u0629 \u0627\u0644\u062A\u0641\u0627\u0636\u0644\u064A\u0629 \u0627\u0644\u0623\u0635\u0644\u064A\u0629 \u0648\u062D\u0644 \u0627\u0644\u0645\u0639\u0627\u062F\u0644\u0629 \u0627\u0644\u062A\u0641\u0627\u0636\u0644\u064A\u0629 \u0627\u0644\u0645\u062E\u0637\u0637\u0629 \u0627\u0644\u062A\u0627\u0628\u0639\u0629 \u0644\u0647\u0627 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0633\u0644\u0648\u0643 \u0641\u064A \u0645\u062D\u064A\u0637 \u0646\u0642\u0637\u0629 \u0633\u0643\u0648\u0646 \u0625\u0647\u0644\u064A\u062C\u064A\u0629. \u0648\u0645\u0639\u0646\u0649 \u0646\u0642\u0637\u0629 \u0633\u0643\u0648\u0646 \u0625\u0647\u0644\u064A\u062C\u064A\u0629 \u0647\u0648 \u0623\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0646\u0627\u062A\u062C\u0629 \u0639\u0646 \u062A\u062E\u0637\u064A\u0637 \u0627\u0644\u0646\u0638\u0627\u0645 \u0639\u0646\u062F \u0646\u0642\u0637\u0629 \u0627\u0644\u0633\u0643\u0648\u0646 \u0644\u0627 \u062A\u062D\u062A\u0648\u064A \u0639\u0644\u0649 \u0642\u064A\u0645 \u0630\u0627\u062A\u064A\u0629 \u064A\u0643\u0648\u0646 \u0627\u0644\u062C\u0632\u0621 \u0627\u0644\u062D\u0642\u064A\u0642\u064A \u0645\u0646\u0647\u0627 \u0635\u0641\u0631\u0627."@ar . . "Satz von Hartman-Grobman"@de . . . "A matem\u00E0tiques, a l'estudi de sistemes din\u00E0mics, el teorema de Hartman-Grobman o el teorema de linelitzaci\u00F3 \u00E9s el teorema que tracta del comportament local del sistema al voltant d'un punt d'equilibri. B\u00E0sicament, el teorema anuncia que el comportament del sistema din\u00E0mic prop d'un punt d'equilibri \u00E9s qualitativament el mateix que el comportament que la seva linealitzaci\u00F3 prop del mateix punt d'equilibri si i nom\u00E9s si tots els valors propis de la linealitzaci\u00F3 tenen part real diferent de zero."@ca . . . .