{"id":37592,"date":"1998-01-01T00:00:00","date_gmt":"1998-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/integrability-normalization-and-symmetries-of-hamiltonian-systems-in-1-1-1-resonance\/"},"modified":"1998-01-01T00:00:00","modified_gmt":"1998-01-01T00:00:00","slug":"integrability-normalization-and-symmetries-of-hamiltonian-systems-in-1-1-1-resonance","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/integrability-normalization-and-symmetries-of-hamiltonian-systems-in-1-1-1-resonance\/","title":{"rendered":"Integrability, normalization and symmetries of hamiltonian systems in 1-1-1 resonance."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Patricia Yanguas Sayas <\/strong><\/h2>\n<p>En esta tesis se aborda el estudio de la resonancia 1-1-1. Concretamente, tratamos el comportamiento de un flujo hamiltoniano en torno a un equilibrio el\u00edptico en el espacio tridimensional. La funci\u00f3n hamiltoniana que representa al sistema din\u00e1mico se descompone en la suma de una parte principal, que corresponde a la vibraci\u00f3n de tres osciladores arm\u00f3nicos y una peque\u00f1a perturbaci\u00f3n de tipo polin\u00f3mico c\u00fabico en las variables cartesianas. La idea b\u00e1sica es convertir el hamiltoniano de partida en uno equivalente pero 7bas f\u00e1cil de estudiar. De este modo se extraen conclusiones del sistema reducido, que son aplicables al original en ciertas condiciones. Tras la reducci\u00f3n por la simetr\u00eda del oscilador llegamos al espacio cp2 que es descrito por nueve invariantes. En los problemas que gozan de una simetr\u00eda axial se puede efectuar otra reducci\u00f3n pasando a un espacio de dimensi\u00f3n dos, que es descrito por tres invariantes. Prestamos especial atenci\u00f3n a estos problemas, clasificando los equilibrios y bifurcaciones en el segundo espacio reducido. De ah\u00ed extraemos como sistema especial el de h\u00e9non y heiles en el espacio, que requeire un tratamiento espec\u00edfico. Las aplicaciones se encuentran por ejemplo, en din\u00e1mica gal\u00e1ctica y molecular.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Integrability, normalization and symmetries of hamiltonian systems in 1-1-1 resonance.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Integrability, normalization and symmetries of hamiltonian systems in 1-1-1 resonance. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Patricia Yanguas Sayas <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 P\u00fablica de navarra<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1998<\/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>Sebastian Ferrer Martinez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jaume Llibre <\/li>\n<li>Antonio Elipe (vocal)<\/li>\n<li>Alberto Ibort Ines (vocal)<\/li>\n<li>Heinz Hanbmann (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Patricia Yanguas Sayas En esta tesis se aborda el estudio de la resonancia 1-1-1. Concretamente, tratamos el [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[3183,12585,126,18529],"tags":[98368,98367,98369,88276,98366,70529],"class_list":["post-37592","post","type-post","status-publish","format-standard","hentry","category-analisis-y-analisis-funcional","category-ecuaciones-diferenciales-ordinarias","category-matematicas","category-publica-de-navarra","tag-alberto-ibort-ines","tag-antonio-elipe","tag-heinz-hanbmann","tag-jaume-llibre","tag-patricia-yanguas-sayas","tag-sebastian-ferrer-Martinez"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/37592","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=37592"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/37592\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=37592"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=37592"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=37592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}