{"id":42888,"date":"2018-03-09T09:45:01","date_gmt":"2018-03-09T09:45:01","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/aplicacion-de-metodos-algebraicos-y-geometricos-al-estudio-de-la-evolucion-de-sistemas-dinamicos\/"},"modified":"2018-03-09T09:45:01","modified_gmt":"2018-03-09T09:45:01","slug":"aplicacion-de-metodos-algebraicos-y-geometricos-al-estudio-de-la-evolucion-de-sistemas-dinamicos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/aplicacion-de-metodos-algebraicos-y-geometricos-al-estudio-de-la-evolucion-de-sistemas-dinamicos\/","title":{"rendered":"Aplicacion de metodos algebraicos y geometricos al estudio de la evolucion de sistemas dinamicos."},"content":{"rendered":"<h2>Tesis doctoral de <strong> JavierA. Nasarre Aznarez <\/strong><\/h2>\n<p>El objetivo de la tesis es aplicar los m\u00e9todos algebraicos y geom\u00e9tricos modernos al estudio de los sistemas din\u00e1micos y, en particular, al estudio de los sistemas de ecuaciones diferenciales que los definen.  la tesis est\u00e1 estructurada en cuatro cap\u00edtulos. En el primer cap\u00edtulo se enmarca el problema a estudiar. De este modo en \u00e9l se estudian las estructuras geom\u00e9tricas que definen los sistemas de ecuaciones diferenciales, en particular, los sistemas no auton\u00f3mos y no lineales, as\u00ed como se presenta su aplicaci\u00f3n a los sistemas hamiltomianos dependientes del tiempo.  en el segundo cap\u00edtulo se estudian de forma paralela el teorema de lie-scheffers y el m\u00e9todo de wei-norman de ecuaciones diferenciales, interpretando ambas desde el punto de vista geom\u00e9trico y algebraico. Adem\u00e1s se aplica todo lo anterior al estudio de la ecuaci\u00f3n de riccati y de un sistema de ecuaciones diferenciales no lineales. Por \u00faltimo se da una aplicaci\u00f3n en el campo de la mec\u00e1nica cu\u00e1ntica: la resoluci\u00f3n del problema espectral del oscilador arm\u00f3nico.  en el tercer cap\u00edtulo se presentan diversos m\u00e9todos de resoluci\u00f3n aproximada de ecuaciones diferenciales. En particular se presentan los m\u00e9todos de dragt-forest, magnus, fer y fer-wilox, todos ellos comparten de caracter\u00edstica de conservar la simplecticidad o unitaridad de las estructuras sobre los que act\u00faan.  el \u00faltimo cap\u00edtulo est\u00e1 dedicado al estudio de la \u00f3ptica simpl\u00e9ctica. En \u00e9l se fundamentan rigurosamente las estructuras geom\u00e9tricas del espacio de rayos y se hallan coordenadas de darboux en diversos medios \u00f3pticos. Por \u00faltimo se aplican los m\u00e9todos perturbativos presentados en el cap\u00edtulo anterior al estudio de la evoluci\u00f3n del rayo \u00f3ptico.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Aplicacion de metodos algebraicos y geometricos al estudio de la evolucion de sistemas dinamicos.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Aplicacion de metodos algebraicos y geometricos al estudio de la evolucion de sistemas dinamicos. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 JavierA. Nasarre Aznarez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Zaragoza<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 30\/04\/1999<\/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> Cari\u00f1ena Marzo Jos\u00e9 F.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Miguel Carlos Mu\u00f1oz lecanda <\/li>\n<li>Mar\u00eda no Santander navarro (vocal)<\/li>\n<li>Alberto Ibort latre (vocal)<\/li>\n<li>Luis lorenzo S\u00e1nchez soto (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de JavierA. Nasarre Aznarez El objetivo de la tesis es aplicar los m\u00e9todos algebraicos y geom\u00e9tricos modernos al [&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":[1191,199,1432,583,126,31342,13610],"tags":[6173,95468,107463,6800,28980,30560],"class_list":["post-42888","post","type-post","status-publish","format-standard","hentry","category-analisis-numerico","category-fisica","category-fisica-teorica","category-geometria","category-matematicas","category-resolucion-de-ecuaciones-diferenciales","category-zaragoza","tag-alberto-ibort-latre","tag-carinena-marzo-jose-f","tag-javiera-nasarre-aznarez","tag-luis-lorenzo-sanchez-soto","tag-maria-no-santander-navarro","tag-miguel-carlos-munoz-lecanda"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/42888","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=42888"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/42888\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=42888"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=42888"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=42888"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}