{"id":36455,"date":"1998-01-01T00:00:00","date_gmt":"1998-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/punts-singulars-i-orbites-periodiques-per-a-camps-vectorials\/"},"modified":"1998-01-01T00:00:00","modified_gmt":"1998-01-01T00:00:00","slug":"punts-singulars-i-orbites-periodiques-per-a-camps-vectorials","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/punts-singulars-i-orbites-periodiques-per-a-camps-vectorials\/","title":{"rendered":"Punts singulars i orbites periodiques per a camps vectorials."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Joan Torregrosa Ar\u00fas <\/strong><\/h2>\n<p>En la teor\u00eda cualitativa de las ecuaciones diferenciales en el plano, conocer el n\u00famero de ciclos l\u00edmite que puede presentar una familia concreta, es desde los tiempos de h. Poincar\u00e9 un problema abierto. En esta memoria se estudian, principalmente, las posibles respuestas para las dos preguntas siguientes: cuantos ciclos l\u00edmite se pueden generar del origen en el caso de una bifurcaci\u00f3n degenerada de hopf, en el caso de que el origen sea de tipo monodr\u00f3mico? Cuantos ciclos l\u00edmite se obtienen al perturbar el hamiltoniano h=1\/2 (x2+y2)? El primer cap\u00edtulo est\u00e1 dedicado al estudio de las condiciones necesarias para que un sistema tenga un centro en el origen, desarrollando un nuevo m\u00e9todo para este efecto.  en el cap\u00edtulo 2, se dan respuestas a las preguntas mencionadas para algunas familias de ecuaciones diferenciales, por ejemplo las ecuaciones de li\u00e9nard, y las familias homog\u00e9neas. Los m\u00e9todos introducidos en los cap\u00edtulos anteriores permiten, en el cap\u00edtulo 3, dar la forma de las \u00f3rbitas peri\u00f3dicas en funci\u00f3n del par\u00e1metro de perturbaci\u00f3n, y se usan para estudiar el problema del centro para el caso de sistemas anal\u00edticos a trozos. Los cap\u00edtulos 4 y 5 se dedican al estudio de la ecuaci\u00f3n de li\u00e9nard. En estos se consigue generalizar un criterio para la caracterizaci\u00f3n de centros para el caso degenerado. Adem\u00e1s, se estudia el m\u00e1ximo orden de degeneraci\u00f3n que puede presentar el origen, a partir de calcular la multiplicidad en el origen de una aplicaci\u00f3n, y con este, mejorar las cotas conocidas para este n\u00famero.  en el \u00faltimo cap\u00edtulo, se estudia la relaci\u00f3n que existe entre la multiplicidad y el \u00edndice de una aplicaci\u00f3n en un cero de esta.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Punts singulars i orbites periodiques per a camps vectorials.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Punts singulars i orbites periodiques per a camps vectorials. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Joan Torregrosa Ar\u00fas <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1998<\/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>Armengol Gasull Embid<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jaume Llibre Salo <\/li>\n<li>Xavier Chavarriga Soriano (vocal)<\/li>\n<li>Carles Sim\u00f3 Torres (vocal)<\/li>\n<li>Hector Giacomini (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Joan Torregrosa Ar\u00fas En la teor\u00eda cualitativa de las ecuaciones diferenciales en el plano, conocer el n\u00famero [&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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