{"id":30971,"date":"2018-03-09T09:24:49","date_gmt":"2018-03-09T09:24:49","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/reducibility-of-quasi-periodic-skew-products-and-the-spectrum-of-schra%c2%b6dinger-operators\/"},"modified":"2018-03-09T09:24:49","modified_gmt":"2018-03-09T09:24:49","slug":"reducibility-of-quasi-periodic-skew-products-and-the-spectrum-of-schra%c2%b6dinger-operators","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/barcelona\/reducibility-of-quasi-periodic-skew-products-and-the-spectrum-of-schra%c2%b6dinger-operators\/","title":{"rendered":"Reducibility of quasi-periodic skew-products and the spectrum of schr\u00c1\u00b6dinger operators"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Joaquim Puig Sadurn\u00ed <\/strong><\/h2>\n<p>En esta tesis estudiamos la reducibilidad y otras propiedades din\u00e1micas de \u00abskew-productos\u00bb lineales cuasiperi\u00f3dicos, especialmente aquellos que provienen de ecuaciones de valores propios de operadores unidimensionales y cuasiperi\u00f3dicos de schr\u00ed\u00b6dinger. Para ello, combinamos m\u00e9todos din\u00e1micos y espectrales para dar un enfoque unificado y nuevos resultados, tanto desde el punto de vista din\u00e1mico como el espectral. Como ejemplo de esta combinaci\u00f3n, en esta tesis demostramos el \u00abproblema de los diez martinis\u00bb propuesto en 1981 por kac y simon.  los dos primeros cap\u00edtulos contiene preliminares, mientras que los otros cuatro resultados novedosos. En el primero introducimos conceptos b\u00e1sicos como los \u00abskew-products\u00bb y cociclos cuasiperi\u00f3dicos, la reducibilidad a coeficientes constantes y la teor\u00eda espectral de sacker-sell. El segundo acp\u00edtulo se centra en los operadores de schr\u00ed\u00b6dinger, ya sean continuos o discretos, y sus ecuaciones de valores propios, que llamamos ecuaci\u00f3n de hill cuasiperi\u00f3dica (en el caso continuo) o de tipo harper (en el caso discreto).  el tercero y el cuarto cap\u00edtulos tratan de la estructura de las llamadas \u00ablenguas de resonancia\u00bb en ecuaciones de hill cuasiperi\u00f3dicas cuyos potenciales son anal\u00edticos reales, peque\u00f1os y con frecuencias diof\u00e1nticas. Desde el punto de vista de operadores de schr\u00ed\u00b6dinger, este estudio es equivalente a la de la estructura de los agujeros espectrales en el espectro de dichos operadores. En el tercer cap\u00edtulo, se usa la  teor\u00eda de formas normales para mostrar la diferenciabilidad infinita de las fronteras de las lenguas de resonancia de un modo constructivo. En el cuarto, demostramos el car\u00e1cter anal\u00edtico real de estas, usando un m\u00e9todo kam que puede adaptarse en otros modelos. Como aplicaci\u00f3n demostramos la genericidad de \u00abtener todos los agujeros abiertos\u00bb para operadores cuasiperi\u00f3dicos de schr\u00ed\u00b6dinger.  en el quinto y sexto cap\u00edtulos estudiamos operadores cuasip<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Reducibility of quasi-periodic skew-products and the spectrum of schr\u00c1\u00b6dinger operators<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Reducibility of quasi-periodic skew-products and the spectrum of schr\u00c1\u00b6dinger operators <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Joaquim Puig Sadurn\u00ed <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 22\/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>Carles Sim\u00f3 Torres<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: angel Jorba montes <\/li>\n<li>hakan Eliasson (vocal)<\/li>\n<li>henk Broer (vocal)<\/li>\n<li>Rafael De la llave canaso (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Joaquim Puig Sadurn\u00ed En esta tesis estudiamos la reducibilidad y otras propiedades din\u00e1micas de \u00abskew-productos\u00bb lineales cuasiperi\u00f3dicos, [&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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