{"id":72018,"date":"2018-03-09T23:16:46","date_gmt":"2018-03-09T23:16:46","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/contribution-to-the-qualitative-study-of-planar-differential-systems\/"},"modified":"2018-03-09T23:16:46","modified_gmt":"2018-03-09T23:16:46","slug":"contribution-to-the-qualitative-study-of-planar-differential-systems","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/contribution-to-the-qualitative-study-of-planar-differential-systems\/","title":{"rendered":"Contribution to the qualitative study of planar differential systems"},"content":{"rendered":"<h2>Tesis doctoral de <strong> M.teresa Grau Monta\u00f1a <\/strong><\/h2>\n<p>Esta tesis se sit\u00faa en el marco de la teor\u00eda cualitativa de los sistemas diferenciales en el plano. Caca cap\u00edtulo contine un aspecto distinto. En la introducci\u00f3n, se da un resumen de los resultados conocidos y se presenta la notaci\u00f3n usada durante el resto de la tesis.  en particular, se describe el problema de la integrabilidad y algunos resultados referentes a la determinaci\u00f3n de la estabilidad de un punto singular a una \u00f3rbia peri\u00f3dica con el fin de introducir los \u00faltimos cap\u00edtulos. Definimos el problema de la integrabilidad como el problema de encontrar una integral primera para un sistema diferencial plano y determinar la clase funcional a la cual \u00e9sta debe pertenecer. Los cap\u00edtulos 2 y 3 tratan sobre el problema de la integrabilidad.  en el cap\u00edtulo 2, obtenemos un resultado que permite encontrar una expresi\u00f3n expl\u00edcita para una integral primera para un cierto tipo de sistema polinomial. mediante un cambio racional de variable, hacemos corresponder una ecuaci\u00f3n diferencial lineal homog\u00e9nea de segundo orden: a2 (x) w'(x) + al (x) + a0 (x) w (x)  = 0, cuyos coeficientes son polinomios, a un sistema diferencial polinomial en el plano. Probamos que dicho sistema tiene un invariante para cada soluci\u00f3n arbitraria no nula w(x) de la edo de segundo orden, que, en caso que w(x) sea un polinomio, da lugar a una curva algebraica invariante. Adem\u00e1s, damos una expresi\u00f3n expl\u00edcita de una integral primera para el sistema construida a partir de dos soluciones independientes de la edo de segundo orden. Esta integral primera no es, en general, una funic\u00f3n liouvilliana.  finalmente, verificamos que todos los ejemplos conocidos de familias de sistemas cuadr\u00e1ticos con una curva algebraica invariante de grado arbitrariamente alto se pueden describir mediante esta construcci\u00f3n (m\u00f3dulo transformaciones birracionales).  en el cap\u00edtulo 3, las curvas algebraicas invariantes de un sistema diferencial plano polinomial juegan un pa<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Contribution to the qualitative study of planar differential systems<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Contribution to the qualitative study of planar differential systems <\/li>\n<li><strong>Autor:<\/strong>\u00a0 M.teresa Grau Monta\u00f1a <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 17\/12\/2004<\/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: armengol Gasull embid <\/li>\n<li>jaume Gin\u00e9 mesa (vocal)<\/li>\n<li>jean Moulin-ollagnier (vocal)<\/li>\n<li>Rafael Prohens sastre (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de M.teresa Grau Monta\u00f1a Esta tesis se sit\u00faa en el marco de la teor\u00eda cualitativa de los sistemas [&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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