{"id":74004,"date":"2018-03-09T23:18:57","date_gmt":"2018-03-09T23:18:57","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/on-the-algebraic-limit-cycles-of-quadratic-systems\/"},"modified":"2018-03-09T23:18:57","modified_gmt":"2018-03-09T23:18:57","slug":"on-the-algebraic-limit-cycles-of-quadratic-systems","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/on-the-algebraic-limit-cycles-of-quadratic-systems\/","title":{"rendered":"On the algebraic limit cycles of quadratic systems"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jordi Sorolla Bardaj\u00ed <\/strong><\/h2>\n<p>Encontramos todos los sistemas cuadr\u00e1ticos (grado 2) que pueden dejar invariante una curva de grado menor o igual que 4 contenga un \u00f3valo que sea, a su vez, cilclo l\u00edmite del sistema. Primero hacemos un estudio de las posibles curvas en funci\u00f3n de sus puntos de autoinsercci\u00f3n (puntos m\u00faltiples). Luego, llegamos a una aproximaci\u00f3n de la forma de la curva a partir de ciertas propiedades de los \u00edndices de intersecci\u00f3n en los puntos singulares y su localizaci\u00f3n. Finalmente, comprobamos si puede ser invariante por un sistema cuadr\u00e1tico y acabamos de ajustar los par\u00e1metros que quedan libres.  tambi\u00e9n estudiamos los ciclos l\u00edmite desde el punto de vista de los sistemas en lugar de desde las curvas invariantes. As\u00ed, tomamos los sistemas cuadr\u00e1ticos que pueden tener ciclos l\u00edmite, concretamente la clasificaci\u00f3n china (familias i, ii y iii). Para la familia i buscamos curvas invariantes e inversos de factor integrante: para las familias ii y iii buscamos inversos de integrante. acabamos demostrando que la familia i no tiene ciclos l\u00edmites algebracios.  finalmente, estudiamos la coexistencia de dos ciclos l\u00edmites algebraicos, que pertenezcan a curvas invariantes irreducibles diferentes, en un sistema cuadr\u00e1tico. Se demuestra que estos ciclos l\u00edmite deber\u00e1n estar contenidos uno en el interior del otro. La demostraci\u00f3n pasa por ver que si estos ciclos defnieran regiones que no se intersecasen, entonces estudiando los valores del cofactor en los puntos singulares vemos que se podr\u00eda construir un inverso de factor integrante polinomial que ser\u00eda el producto de las dos curvas y que dar\u00eda lugar a una integral primera de tipo darboux, lo cual lleva a una contradicci\u00f3n.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>On the algebraic limit cycles of quadratic systems<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 On the algebraic limit cycles of quadratic systems <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jordi Sorolla Bardaj\u00ed <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 17\/05\/2005<\/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: jaume Libres sal\u00f3 <\/li>\n<li>h\u00e9ctor Giacomini (vocal)<\/li>\n<li>isaac Antonio Garcia rodriguez (vocal)<\/li>\n<li>sebasti\u00e1n Walcher (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jordi Sorolla Bardaj\u00ed Encontramos todos los sistemas cuadr\u00e1ticos (grado 2) que pueden dejar invariante una curva de [&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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