{"id":30781,"date":"2018-03-09T09:24:33","date_gmt":"2018-03-09T09:24:33","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/multiplicidades-algebraicas-y-teoria-de-bifurcacion\/"},"modified":"2018-03-09T09:24:33","modified_gmt":"2018-03-09T09:24:33","slug":"multiplicidades-algebraicas-y-teoria-de-bifurcacion","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/multiplicidades-algebraicas-y-teoria-de-bifurcacion\/","title":{"rendered":"Multiplicidades algebraicas y teor\u00eda de bifurcaci\u00f3n"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Carlos Mora Corral <\/strong><\/h2>\n<p>Se profundiza en el concepto de multiplicidad algebraica de una familia uniparam\u00e9trica de operadores de fredholm de \u00edndice cero en un punto del par\u00e1metro donde la familia deja de ser invertible. Probamos un resultado de unicidad de la multiplicidad. Generalizamos al caso real propiedades conocidas en el caso complejo: en particular, la existencia de forma local de smith y la posibilidad de calcular la multiplicidad mediante un residuo logar\u00edtmico.  en lo que concierne a teor\u00eda local de difurcaci\u00f3n, la forma local de smith se usa para caracterizar los autovalores no lineales en un problema de bifurcaci\u00f3n, es decir, para caracterizar aquellos autovalores de la linealizaci\u00f3n para los cuales siempre existe difurcaci\u00f3n idependientemente de la parte no lineal (t\u00e9rminos de orden superior). En teor\u00eda global de bifurcaci\u00f3n genralizamos resultados cl\u00e1sicos de rabinowitz, ize, dancer y magnus relativos a las componentes acotadas de soluciones no triviales. No suponemos que el conjunto de autovalores de la familia linealizada sea discreto, trabajamos con componentes semiacotadas (es decir, acotadas en una direcci\u00f3n del par\u00e1metro), pero que pudieran no ser acotadas en todo el espacio. Damos estimaciones inferiores del n\u00famero de soluciones de las secciones (obtenidas fijando un valor del par\u00e1metro) de las componentes semiacotadas de soluciones no triviales, esto se hace calculando el grado topol\u00f3gico en dichas secciones a trav\u00e9s \u00fanicamente de los puntos de bifurcaci\u00f3n de dicha componente.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Multiplicidades algebraicas y teor\u00eda de bifurcaci\u00f3n<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Multiplicidades algebraicas y teor\u00eda de bifurcaci\u00f3n <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Carlos Mora Corral <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Complutense de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 16\/06\/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>Julian Lopez Gomez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  L\u00f3pez vel\u00e1zquez Juan  jos\u00e9 <\/li>\n<li>jonathan Magnus robert (vocal)<\/li>\n<li>israel Gohberg (vocal)<\/li>\n<li>jean Mawhin (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Carlos Mora Corral Se profundiza en el concepto de multiplicidad algebraica de una familia uniparam\u00e9trica de operadores [&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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