{"id":25577,"date":"2018-03-09T09:17:01","date_gmt":"2018-03-09T09:17:01","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/on-symplectic-linearization-of-singular-lagrangian-foliations\/"},"modified":"2018-03-09T09:17:01","modified_gmt":"2018-03-09T09:17:01","slug":"on-symplectic-linearization-of-singular-lagrangian-foliations","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/on-symplectic-linearization-of-singular-lagrangian-foliations\/","title":{"rendered":"On symplectic linearization of singular lagrangian foliations"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Eva Miranda Galcer\u00e1n <\/strong><\/h2>\n<p>En esta tesis se estudia el problema de clasificaci\u00f3n de estructuras simpl\u00e9cticas definidas en un entorno de una \u00f3rbita singular compacta de un sistema completamente integrable sobre una variedad simpl\u00e9ctica para las cuales la foliaci\u00f3n determinada por la aplicaci\u00f3n momento es gen\u00e9ricamente lagrangiana. Dicha foliaci\u00f3n est\u00e1 determinada por las \u00f3rbitas de la distribuci\u00f3n generada por los gradientes simpl\u00e9cticos de las componentes de la aplicaci\u00f3n momento $f$. En dicho estudio suponemos que la aplicaci\u00f3n momento es una aplicaci\u00f3n propia y que la singularidad es no-degenerada en el sentido de morse-bolt. los invariantes diferenciables para dicha foliaci\u00f3n vienen determinados por el rango de la \u00f3rbita, el tipo de williamson y un grupo \u00abtwisting\u00bb actuando sobre las componentes hiperb\u00f3licas. Dichos invariantes determinan un modelo lineal diferenciable para la foliaci\u00f3n. Bajo estas hip\u00f3tesis demostramos que dadas dos estructuras simpl\u00e9cticas $\/omega_1$ y $\/omega_2$ para las cuales la foliaci\u00f3n es gen\u00e9ricamente lagrangiana son equivalentes en el sentido siguiente: existe un difeomorfismo definido en un entorno de la \u00f3rbita singular compacta preservando la foliaci\u00f3n y enviando $\/omega_1$ a $\/omega_2$.  en el caso en que exista una acci\u00f3n simpl\u00e9ctica de un grupo de lie compacto $g$ que conserva la aplicaci\u00f3n momento $f$, probamos que existe un difeomorfismo cumpliendo las condiciones anteriores y que adem\u00e1s dicho difeomorfismo puede construirse de forma $g$-equivariante.  en esta tesis tambi\u00e9n damos una aplicaci\u00f3n de este resultado de clasificaci\u00f3n en geometr\u00eda de contacto.  consideramos una variedad de contacto para la cual el campo de reeb admite $n$ integrales gen\u00e9ricamente idenpendientes y conmutando respecto el par\u00e9ntesis de jacobi y suponemos que dichas $n$ integrales determinan una aplicaci\u00f3n propia. Las componentes horizontales de los campos de vectores de contacto asociados a estas integrales, determin<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>On symplectic linearization of singular lagrangian foliations<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 On symplectic linearization of singular lagrangian foliations <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Eva Miranda Galcer\u00e1n <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 22\/09\/2003<\/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 Curras Bosch<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: angel Jorba montes <\/li>\n<li>zung Nguyen tien (vocal)<\/li>\n<li>agusti Reventos tarrida (vocal)<\/li>\n<li>viktor Ginzburg (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Eva Miranda Galcer\u00e1n En esta tesis se estudia el problema de clasificaci\u00f3n de estructuras simpl\u00e9cticas definidas 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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