{"id":53599,"date":"2018-03-09T22:41:16","date_gmt":"2018-03-09T22:41:16","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/homogeneous-polynomial-vector-fields-on-the-2-dimensional-sphere\/"},"modified":"2018-03-09T22:41:16","modified_gmt":"2018-03-09T22:41:16","slug":"homogeneous-polynomial-vector-fields-on-the-2-dimensional-sphere","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/homogeneous-polynomial-vector-fields-on-the-2-dimensional-sphere\/","title":{"rendered":"Homogeneous polynomial vector fields on the 2-dimensional sphere"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Claudio Gomes Pessoa <\/strong><\/h2>\n<p>La teor\u00eda de los sistemas din\u00e1micos es una de las m\u00e1s importantes herramientas para estudiar  cualitativamente e cuantitativamente los modelos de las ciencias aplicadas. Desde los primeros trabajos publicados por poincar\u00e9, a teor\u00eda de las ecuaciones diferenciales ordinarias tiene experimentado una expansi\u00f3n significativa envolviendo t\u00e9cnicas de casi todas las \u00e1reas de la matem\u00e1tica. Dentro de esta  teor\u00eda los campos de vectores definidos en el plano o en una superficie tienen sido unos de los principales objetos estudiados. Sin embargo est\u00e9s t\u00f3picos est\u00e1n lejos de estar totalmente entendidos. problemas famosos en este t\u00f3pico son el 16\u00c2\u00ba problema de hilbert, el problema del centro-foco, el problema de la integrabilidad, etc. Recientemente nuevos conocimientos  sobre la teor\u00eda de integrabilidad de darboux  e sobre curvas algebraicas invariantes proporcionaron importantes contribuciones para algunos de estos problemas.  en nuestro trabajo consideramos campos de vectores polinomiales homog\u00e9neos en la 2-dimensional esfera. Estudiamos sus c\u00edrculos invariantes, o sea curvas algebraicas invariantes en la esfera sobre el flujo asociado a tales campos de vectores formados por c\u00edrculos. Determinamos cotas superiores para el n\u00famero m\u00e1ximo de c\u00edrculos invariantes de un campo de vectores polinomial homog\u00e9neo en la esfera en funci\u00f3n de su grado,  cuando este numero es finito. adem\u00e1s, proporcionamos casi una clasificaci\u00f3n global de todos los retratos de fase de campos de vectores polinomiales   homog\u00e9neos en la esfera de grado 2. Para hacer esto la principal herramienta que usamos es la teor\u00eda cualitativa de campos de vectores en el plano, pues los campos de vectores polinomiales   homog\u00e9neos en la esfera de grado 2 pueden ser reducidos a lo estudio de una familia de campos de vectores en el plano de grado 3 con seis par\u00e1metros.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Homogeneous polynomial vector fields on the 2-dimensional sphere<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Homogeneous polynomial vector fields on the 2-dimensional sphere <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Claudio Gomes Pessoa <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 29\/06\/2006<\/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>Jaume Llibre Salo<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: armengol Gasull embid <\/li>\n<li>jaume Gin\u00e9 mesa (vocal)<\/li>\n<li>weigu Li (vocal)<\/li>\n<li>jordi Villadelprat yag\u00ed\u00bce (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Claudio Gomes Pessoa La teor\u00eda de los sistemas din\u00e1micos es una de las m\u00e1s importantes herramientas para [&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 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