{"id":31780,"date":"1997-01-01T00:00:00","date_gmt":"1997-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/contribution-to-the-integrability-of-systems-of-ordinary-differential-equations-in-the-plane-with-linear-part-of-center-type\/"},"modified":"1997-01-01T00:00:00","modified_gmt":"1997-01-01T00:00:00","slug":"contribution-to-the-integrability-of-systems-of-ordinary-differential-equations-in-the-plane-with-linear-part-of-center-type","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/contribution-to-the-integrability-of-systems-of-ordinary-differential-equations-in-the-plane-with-linear-part-of-center-type\/","title":{"rendered":"Contribution to the integrability of systems of ordinary differential equations in the plane with linear part of center type."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jaume Gine Mesa <\/strong><\/h2>\n<p>El principal objetivo de esta memoria es el estudio de la integrabilidad de los sistemas de ecuaciones diferenciales ordinarias en el plano de la forma:     x.  = -y + landa x + x(x,y), y. = X + y(x,y),  (1) donde x(x,y) y y(x,y) son funciones analiticas en un cierto entorno del origen y cuyo desarrollo en serie de potencias carece de terminos constantes y lineales.  objetivos secundarios han sido la determinacion y construccion de sistemas de la forma (1) con ciclos limite y el comportamiento de estos sistemas ak variar ciertos parametros significativos.  los principales resultados que se han obtenido son: la clasificacion de los casos integrables cuando landa=0 y x(x,y) y y(x,y) son polinomios homogeneos de grados cuarto y quinto, la determinacion de sistemas de la forma (1) que admiten integrales primeras polinomiales globales, la total caracterizacion de los sistemas de la forma (1) donde x(x,y) y y(x,y) son polinomios cubicos con el infinito degenerado, la clasificacion de los centros isocronos del sistema (1) cuando x(x,y) y y(x,y) son polinomios homogeneos de grados cuarto y quinto, la total clasificacion de los centros isocronos del sistema (1) cuando x(x,y) y y(x,y) son polinomios cubicos con el infinito degenerado, la existencia de una nueva bifurcacion degenerada para sistemas de la forma (1) donde x(x,y) y y(x,y) son polinomios cubicos, la construccion de nuevos sistemas integrables a partir de sistemas integrables dados, la determinacion de nuevos casos de integrabilidad para sistemas de la forma (1) siendo x(x,y) y y(x,y) polinomios cubicos y, finalmente, la caracterizacion de los casos integrables de sistemas de la forma x. = Xn(x,y) + xm(x,y), y. = Yn(x,y) + ym(x,y), donde xk(x,y) y yk(x,y) son quasi-homogeneos polinomios de grados rerspectivos k-q+2pq-1 y k-p+2pq-1 con m mayor que n siendo k = (m,n).<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Contribution to the integrability of systems of ordinary differential equations in the plane with linear part of center type.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Contribution to the integrability of systems of ordinary differential equations in the plane with linear part of center type. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jaume Gine Mesa <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de catalunya<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1997<\/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>Javier Chavarriga Soriano<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Amadeu Delhams Valdes <\/li>\n<li>Hector Giacomini (vocal)<\/li>\n<li>Jaume Llibre (vocal)<\/li>\n<li>G. Lloyd Noel (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jaume Gine Mesa El principal objetivo de esta memoria es el estudio de la integrabilidad de los [&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":[1191,3183,12585,126,15596,16115],"tags":[88274,88277,88275,88273,88276,29388],"class_list":["post-31780","post","type-post","status-publish","format-standard","hentry","category-analisis-numerico","category-analisis-y-analisis-funcional","category-ecuaciones-diferenciales-ordinarias","category-matematicas","category-politecnica-de-catalunya","category-resolucion-de-ecuaciones-diferenciales-ordinarias","tag-amadeu-delhams-valdes","tag-g-lloyd-noel","tag-hector-giacomini","tag-jaume-gine-mesa","tag-jaume-llibre","tag-javier-chavarriga-soriano"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/31780","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=31780"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/31780\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=31780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=31780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=31780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}