{"id":85493,"date":"2018-03-10T00:09:57","date_gmt":"2018-03-10T00:09:57","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/clasificacion-de-sistemas-dinamicos-lineales-2-dimensionales-sobre-anillos-conmutativos\/"},"modified":"2018-03-10T00:09:57","modified_gmt":"2018-03-10T00:09:57","slug":"clasificacion-de-sistemas-dinamicos-lineales-2-dimensionales-sobre-anillos-conmutativos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/clasificacion-de-sistemas-dinamicos-lineales-2-dimensionales-sobre-anillos-conmutativos\/","title":{"rendered":"Clasificacion de sistemas dinamicos lineales 2-dimensionales sobre anillos conmutativos"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Andres Saez Schwedt <\/strong><\/h2>\n<p>En este trabajo se estudia la clasificaci\u00f3n de feedback de sistemas din\u00e1micos lineales bidimensionales sobre un anillo conmutativo. Un sistema lineal de dimensi\u00f3n n y m impulsos sobre un anillo conmutativo y unitario r es un par de matrices (f,g) con f e mnxn(r),g e mnxm(r). El grupo de feedback es el conjunto de ternas de matrices (p,q,k):p e g ln(r), q e glm(r),k e mmxn(r), que opera sobre el conjunto de sistemas de tama\u00f1o(n,m) mediante la siguiente acci\u00f3n:  (p,q,k)  (f,g)&#8212;&#8212;-&gt;(pfp-1+pgk,pgq)  dos sistemas son equivalentes feedback si est\u00e1n en la misma orbita por la acci\u00f3n anterior, y nos proponemos hallar formas can\u00f3nicas para la clasificaci\u00f3n de sistemas de esta acci\u00f3n.  un sistema (f,g) se denomina accesible si las columnas de la matriz (g,fg,&#8230;.,Fn-1g) generan rn. A cada ideal i de anillo r, se le asocia un conjunto s i,lo cual para el caso de un ideal principal i=gr permite determinar un sistema completo de formas can\u00f3nicas de sistemas (f,g)2-dimensionales y accesibles con matriz g=(1 0 0&#8230;.0) (*)  (0 g 0&#8230;.0)  si se tiene una factorizaci\u00f3n i=i1&#8230;.It,con i1,&#8230;..It coprimos dos a dos, el c\u00e1lculo de s i se reduce al computo de los conjuntos s it.  cuando el anillo r es un dominio de dedeking, el c\u00e1lculo anterior se reduce al caso en que i es potencia de un ideal primo , y se determinan condiciones suficientes para asegurar la finitud del n\u00famero de clases feedback asociadas a un elemento g fijo. Para los casos particulares r=z y r=r[x], se obtienen de forma expl\u00edcita todas las formas can\u00f3nicas de sistemas 2-dimensionales y accesibles.  si r es el anillo de enteros de un cuerpo de n\u00fameros, los conjuntos sg son finitos( y por lo tanto tambi\u00e9n el nr.De feedback de sistemas accesibles con matriz g como en (*). Dichos conjuntos se calculan de forma expl\u00edcita mediante algoritmos. Para caso de anillos de enteros de cuerpos cuadr\u00e1ticos imaginarios se proporciona una tabla con todas las formas can\u00f3nic<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Clasificacion de sistemas dinamicos lineales 2-dimensionales sobre anillos conmutativos<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Clasificacion de sistemas dinamicos lineales 2-dimensionales sobre anillos conmutativos <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Andres Saez Schwedt <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Valladolid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 30\/06\/2000<\/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>Tom\u00e1s S\u00e1nchez Giralda<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Hermida alonso Jos\u00e9 angel <\/li>\n<li>Emilio Villanueva novoa (vocal)<\/li>\n<li> Bueso montero Jos\u00e9 Luis (vocal)<\/li>\n<li>margarita Rivero alvarez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Andres Saez Schwedt En este trabajo se estudia la clasificaci\u00f3n de feedback de sistemas din\u00e1micos lineales bidimensionales [&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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