{"id":18077,"date":"2002-04-07T00:00:00","date_gmt":"2002-04-07T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/bifurcaciones-en-sistemas-dinamicos-lineales-a-trozos\/"},"modified":"2002-04-07T00:00:00","modified_gmt":"2002-04-07T00:00:00","slug":"bifurcaciones-en-sistemas-dinamicos-lineales-a-trozos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/bifurcaciones-en-sistemas-dinamicos-lineales-a-trozos\/","title":{"rendered":"Bifurcaciones en sistemas din\u00e1micos lineales a trozos"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Victoriano Carmona Centeno <\/strong><\/h2>\n<p>En esta tesis se estudian los sistemas n-dimensionales continuos lineales a trozos definidos en dos zonas (2cpln). Las soluciones de estos sistemas pueden obtenerse de forma expl\u00edcita en cada una de las zonas donde el sistema es lineal, pero el comportamiento din\u00e1mico de tal sistema no es sencillo pues la uni\u00f3n de los flujos de los sistemas lineales que definen al sistema lineal a trozos est\u00e1 lejos de ser trivial.  por otra parte, la falta de diferenciabilidad del sistema impide, en un principio, la aplicaci\u00f3n de las t\u00e9cnicas generales de la din\u00e1mica diferenciable, y por tanto, los sistemas lineales a trozos requieren el uso de t\u00e9cnicas espec\u00edficas que permitan describir su comportamiento din\u00e1mico.  el primer cap\u00edtulo de la memoria considera formas can\u00f3nicas para los sistemas 2cpln, es decir, se obtienen sistemas equivalentes al inicial mediante cambios lineales con un menor n\u00famero de par\u00e1metros y con la pretensi\u00f3n de que resulten m\u00e1s f\u00e1ciles de analizar. Se introducen nuevas formas can\u00f3nicas en las que la no linealidad se concentra en una sola de las ecuaciones del sistema. Seguidamente se estudian las formas can\u00f3nicas a la luz de los conceptos cl\u00e1sicos de la teor\u00eda de control y se proponen nuevas formas, no aparecidas en la literatura, para los sistemas observables y no controlables. en la \u00faltima secci\u00f3n del primer cap\u00edtulo se aplican las formas can\u00f3nicas a los sistemas lineales a trozos con dos y tres variables de estados.  el cap\u00edtulo 2 se centra en el estudio de la aplicaci\u00f3n de poincar\u00e9, definida como la composici\u00f3n de las semiaplicaciones de poincar\u00e9. Se analizan algunas propiedades de la diferencial de tal aplicaci\u00f3n, prestando especial atenci\u00f3n al caso bidimensional.  en el cap\u00edtulo 3 se extiende la teor\u00eda de melmikov a los sistemas planos continuos y diferenciables a trozos. Esta t\u00e9cnicas se emplea con frecuencia en los sistemas 2cpl2, aunque en la literatura tal uso no aparece convenientemen<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Bifurcaciones en sistemas din\u00e1micos lineales a trozos<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Bifurcaciones en sistemas din\u00e1micos lineales a trozos <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Victoriano Carmona Centeno <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Sevilla<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 04\/07\/2002<\/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>Emilio Freire Mac\u00edas<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: rafael Ortega r\u00edos <\/li>\n<li>alejandro Rodr\u00edguez Luis (vocal)<\/li>\n<li>enrique Ponce n\u00fa\u00f1ez (vocal)<\/li>\n<li>armengol Gasull embid (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Victoriano Carmona Centeno En esta tesis se estudian los sistemas n-dimensionales continuos lineales a trozos definidos en [&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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