{"id":100804,"date":"2010-11-05T00:00:00","date_gmt":"2010-11-05T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/existence-and-summability-of-invariant-curves-in-complex-dynamics-in-dimension-two\/"},"modified":"2010-11-05T00:00:00","modified_gmt":"2010-11-05T00:00:00","slug":"existence-and-summability-of-invariant-curves-in-complex-dynamics-in-dimension-two","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/existence-and-summability-of-invariant-curves-in-complex-dynamics-in-dimension-two\/","title":{"rendered":"Existence and summability of invariant curves in complex dynamics in dimension two"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Lorena Lopez Hernanz <\/strong><\/h2>\n<p>En la memoria nos centramos en el estudio de sistemas din\u00e1micos tangentes a la identidad en dimensi\u00f3n dos a trav\u00e9s de su representaci\u00f3n asint\u00f3tica por medio de un campo de vectores formal, el generador infinitesimal. La cuesti\u00f3n b\u00e1sica que motiva nuestro trabajo es comprender hasta qu\u00e9 punto el generador infinitesimal, a pesar de ser un campo formal, representa propiedades de un sistema din\u00e1mico.  presentamos tres resultados principales en esta memoria:  &#8211; existencia de curvas parab\u00f3licas para sistemas din\u00e1micos tangentes a la identidad en dimensi\u00f3n dos con punto fijo aislado. Al igual que en la prueba m\u00e1s laboriosa de m. Abate, partimos de los resultados de m. Hakim y deducimos inmediatamente la existencia, a partir del teorema de camacho y sad y la utilizaci\u00f3n sistem\u00e1tica del diccionario entre sistemas din\u00e1micos y generadores infinitesimales.  &#8211; prueba del car\u00e1cter gevrey en dimensi\u00f3n arbitraria del generador infinitesimal de un sistema din\u00e1mico tangente a la identidad.   &#8211; sumabilidad de las separatrices formales del generador infinitesimal cuando este es de tipo briot y bouquet, probando que las curvas parab\u00f3licas de hakim son las sumas de dichas separatrices. En consecuencia, mediante la proyecci\u00f3n por el morfismo de reducci\u00f3n de singularidades, obtenemos la sumabilidad de las curvas invariantes dadas por el teorema de camacho y sad para el generador infinitesimal de un difeomorfismo tangente a la identidad con punto fijo aislado.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Existence and summability of invariant curves in complex dynamics in dimension two<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Existence and summability of invariant curves in complex dynamics in dimension two <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Lorena Lopez Hernanz <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Valladolid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 11\/05\/2010<\/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>Felipe Cano Torres<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jos\u00e9 manuel Aroca hernandez ros <\/li>\n<li>enmanuel Paul (vocal)<\/li>\n<li>guy Casale (vocal)<\/li>\n<li>anne Duval (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Lorena Lopez Hernanz En la memoria nos centramos en el estudio de sistemas din\u00e1micos tangentes a la [&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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