{"id":72939,"date":"2018-03-09T23:17:47","date_gmt":"2018-03-09T23:17:47","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sobre-la-estabilidad-de-sistemas-hamiltonianos-de-dos-grados-de-libertad-bajo-resonancias\/"},"modified":"2018-03-09T23:17:47","modified_gmt":"2018-03-09T23:17:47","slug":"sobre-la-estabilidad-de-sistemas-hamiltonianos-de-dos-grados-de-libertad-bajo-resonancias","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/sobre-la-estabilidad-de-sistemas-hamiltonianos-de-dos-grados-de-libertad-bajo-resonancias\/","title":{"rendered":"Sobre la estabilidad de sistemas hamiltonianos de dos grados de libertad bajo resonancias."},"content":{"rendered":"<h2>Tesis doctoral de <strong>  Pascual Ler\u00eda Ana  Isabel <\/strong><\/h2>\n<p>La cuesti\u00f3n de la estabilidad de sistemas hamiltonianos es una pieza fundamental en el estudio de algunos problemas de diversas ramas cient\u00edficas, como por ejemplo, de mec\u00e1nica cl\u00e1sica, mec\u00e1nica celeste, f\u00edsica at\u00f3mica, etc. adem\u00e1s, es un tema de gran inter\u00e9s matem\u00e1tico. No obstante, el problema es dif\u00edcil de abordar incluso para sistemas de dos grados de libertad donde, a pesar de ser el caso m\u00e1s simple y donde m\u00e1s estudios hay realizados, todav\u00eda quedan situaciones especiales sin resolver.  pese a la existencia de numerosos problemas de aplicaci\u00f3n y de resultados para algunos casos particulares, hasta 1999 no se enuncia ning\u00fan teorema general. En esta fecha, cabral y meyer establecen un criterio para resolver la estabilidad de un sistema hamiltoniano de dos grados de libertad en presencia de resonancias que engloba a la mayor\u00eda de los resultados cl\u00e1sicos.  la principal aportaci\u00f3n de esta tesis es la obtenci\u00f3n de un teorema que considera hip\u00f3tesis m\u00e1s d\u00e9biles que las del teorema de cabral y meyer, de modo que lo generaliza y permite resolver la cuesti\u00f3n de la estabilidad en condiciones m\u00e1s generales. Adem\u00e1s, damos una interpretaci\u00f3n geom\u00e9trica de este resultado, estableciendo as\u00ed un criterio geom\u00e9trico. A partir de este criterio es posible obtener nuevos resultados de estabilidad para algunos casos que el teorema de cabral y meyer no resuelve, denominados casos degenerados.  el proceso para extraer dichas conclusiones es complicado y exige la utilizaci\u00f3n de un modelo m\u00e1s sencillo, la forma normal del hamiltoniano. Esto supone aplicar t\u00e9cnicas de normalizaci\u00f3n que nosotros hemos llevado a cabo con un conjunto determinado de variables, las variables de lissajous. En este sentido, otra aportaci\u00f3n es una caracterizaci\u00f3n compacta de la forma normal en t\u00e9rminos de unas variables, llamadas invariantes, ligadas a las variables de lissajous.  adem\u00e1s del estudio de la estabilidad es importante la caracteriz<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sobre la estabilidad de sistemas hamiltonianos de dos grados de libertad bajo resonancias.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sobre la estabilidad de sistemas hamiltonianos de dos grados de libertad bajo resonancias. <\/li>\n<li><strong>Autor:<\/strong>\u00a0  Pascual Ler\u00eda Ana  Isabel <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Rioja<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 25\/02\/2005<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>V\u00edctor Lanchares Barrasa<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Antonio Elipe s\u00e1nchez <\/li>\n<li>merc\u00e9 Oll\u00e9 torner (vocal)<\/li>\n<li>Andr\u00e9s Riaguas gued\u00e1n (vocal)<\/li>\n<li>boris Bardin (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Pascual Ler\u00eda Ana Isabel La cuesti\u00f3n de la estabilidad de sistemas hamiltonianos es una pieza fundamental en 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