{"id":17234,"date":"2002-05-06T00:00:00","date_gmt":"2002-05-06T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sistemas-de-lie-y-sus-aplicaciones-en-fa%c2%adsica-y-teoria-de-control\/"},"modified":"2002-05-06T00:00:00","modified_gmt":"2002-05-06T00:00:00","slug":"sistemas-de-lie-y-sus-aplicaciones-en-fa%c2%adsica-y-teoria-de-control","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/sistemas-de-lie-y-sus-aplicaciones-en-fa%c2%adsica-y-teoria-de-control\/","title":{"rendered":"Sistemas de lie y sus aplicaciones en f\u00edsica y teor\u00eda de control"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Arturo Ramos Guti\u00e9rrez <\/strong><\/h2>\n<p>Se estudia la estructura geom\u00e9trica de los llamados sistemas de lie y algunas aplicaciones de tal estudio en f\u00edsica y teor\u00eda de control.  resumimos las principales contribuciones originales de la tesis.  en el cap\u00edtulo 1 se presenta el teorema de lie que caracteriza tales sistemas y se encuentra una acci\u00f3n af\u00edn del grupo de curvas en sl(2,r) sobre el conjunto de ecuaciones de riccati.  en el cap\u00edtulo 2 se formula la teor\u00eda geom\u00e9trica de los sistemas de lie en grupos de lie y espacios homog\u00e9neos. Se generalia la acci\u00f3n af\u00edn anterior al caso de un sistema de lie arbitrario. Se generaliza el m\u00e9todo de wei-norman y se desarrolla una t\u00e9cnica de reducci\u00f3n de sistemas de lie. se establece la relaci\u00f3n de los sistemas de lie con conexiones en fibrados principales y asociados.  en el cap\u00edtulo 3 se ilustra la aplicaci\u00f3n de la teor\u00eda a diferentes sistemas de lie de inter\u00e9s.  en el cap\u00edtulo 4 se aplica la teror\u00eda a problemas de mec\u00e1nica cu\u00e1ntica unidimensional, en concreto a los problemas de operadores entrelazados, transformaciones de darbouz y mec\u00e1nica cu\u00e1ntica supersim\u00e9trica, as\u00ed como a los problemas llamados invariantes de forma.  en el cap\u00edtulo 5 se usa la acci\u00f3n af\u00edn sobre el conjunto de ecuaciones de riccati para explicar el algoritmo de diferencias finitas y el problema de los hamiltonianos entrelazados. Se generalizan las transformaciones de darboux de ecuaciones diferenciales de segundo orden.  en el cap\u00edtulo 6 se aplica la teor\u00eda a sistemas hamiltonianos cl\u00e1sicos y cu\u00e1nticos que adem\u00e1s pueden considerarse como sistemas de lie.  finalmente, en el cap\u00edtulo 7 se muestran aplicaciones en la teor\u00eda geom\u00e9trica de control. Se establecen nuevas relaciones entre sistemas de control, identificando sistemas en base a su estructura algebraica, y por medio de la mencionada t\u00e9cnica de reducci\u00f3n. Se emplea sistem\u00e1ticamente el m\u00e9todo generalizado de wei-norman en tales sistemas.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sistemas de lie y sus aplicaciones en f\u00edsica y teor\u00eda de control<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sistemas de lie y sus aplicaciones en f\u00edsica y teor\u00eda de control <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Arturo Ramos Guti\u00e9rrez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Zaragoza<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 05\/06\/2002<\/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> Cari\u00f1ena Marzo Jos\u00e9 Fernando<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Boya balet Luis joaqu\u00edn <\/li>\n<li>Miguel Carlos Mu\u00f1oz lecanda (vocal)<\/li>\n<li>janusz Grabowski (vocal)<\/li>\n<li>a. Rodr\u00edguez Miguel (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Arturo Ramos Guti\u00e9rrez Se estudia la estructura geom\u00e9trica de los llamados sistemas de lie y algunas aplicaciones [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[199,1432,6264,126,13355,13610],"tags":[54046,54044,28977,6253,54045,30560],"class_list":["post-17234","post","type-post","status-publish","format-standard","hentry","category-fisica","category-fisica-teorica","category-investigacion-operativa","category-matematicas","category-sistemas-de-control","category-zaragoza","tag-a-rodriguez-miguel","tag-arturo-ramos-gutierrez","tag-boya-balet-luis-joaquin","tag-carinena-marzo-jose-fernando","tag-janusz-grabowski","tag-miguel-carlos-munoz-lecanda"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/17234","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=17234"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/17234\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=17234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=17234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=17234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}