{"id":68488,"date":"2008-05-12T00:00:00","date_gmt":"2008-05-12T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/discrete-and-continuous-symmetries-in-planar-vector-fields\/"},"modified":"2008-05-12T00:00:00","modified_gmt":"2008-05-12T00:00:00","slug":"discrete-and-continuous-symmetries-in-planar-vector-fields","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/ecuaciones-diferenciales-ordinarias\/discrete-and-continuous-symmetries-in-planar-vector-fields\/","title":{"rendered":"Discrete and continuous symmetries in planar vector fields"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Susana Maza Sabido <\/strong><\/h2>\n<p>Aquesta tesi es situa en el marc de la teoria qualitativa dels sistemes d#equacions diferencials en el pla. Cada cap\u00edtol cont\u00e9 un aspecte diferent, per\u00ed\u00b2 en tots ells es tracten  problemes, la soluci\u00f3 dels quals est\u00ed\u00a0 basada en el rol que hi juguen les simetries discretes i continues  (reversibilitat o simetries de lie) de camps vectorials plans. A la introducci\u00f3, es d\u00f3na un resum dels resultats m\u00e9s coneguts i s#hi introdueix la notaci\u00f3 que es fa servir al llarg de la tesi.   en el segon i tercer cap\u00edtol, s#aborda el problema de trobar l#expressi\u00f3 expl\u00edcita del canvi linealitzant o orbitalment linealitzant d#un camp vectorial suau a partir del coneixement d#un commutador, en el cas de la linealitzaci\u00f3, o una simetria de lie, en el cas de la linealitzaci\u00f3 orbital. Cada cap\u00edtol finalitza amb exemples il.Lustratius del procediment constructiu dels canvis.  al cap\u00edtol 5 s#apliquen els resultats dels cap\u00edtols anteriors, combinats amb linealitzacions darbouxianes. Concretament, es considera un sistema quadr\u00ed\u00a0tic tipus lotka-volterra i es caracteritzen les selles linealitzables i orbitalment linealitzables mitjan\u00ed\u00a7ant la troballa dels canvis linealitzants o orbitalment linealitzants. en el sis\u00e9 cap\u00edtol, s#utilitza l#exist\u00e9ncia d#un \u00ed\u00a0lgebra de simetries puntuals de lie  per donar informaci\u00f3 sobre l#exist\u00e9ncia i localitzaci\u00f3 d#\u00ed\u00b2rbites peri\u00ed\u00b2diques. En particular, quan l#\u00ed\u00a0lgebra de simetries puntuals de lie d#una equaci\u00f3 diferencial escalar de seg\u00f3n ordre aut\u00ed\u00b2noma i suau t\u00e9 dimensi\u00f3 major o igual a dos, definim les anomenades funcions fonamentals que ens permeten estudiar les \u00ed\u00b2rbites peri\u00ed\u00b2diques al pla de fases. En el cas particular d#equacions polinomials de li\u00e9nard, mostrem la no exist\u00e9ncia de cicles l\u00edmit en tot el pla de fases. finalment, al cap\u00edtol 7 es relacionen els sistemes reversibles amb el problema del centre aix\u00ed com amb el problema de la integrabilitat anal\u00edtica. Considerem sistemes d#equacions diferencials anal\u00edtics amb centres degenerats i mostrem que poden transformar-se, despr\u00e9s d#un reescalat del temps, en un sistema lineal i reversible. El coneixement de integrals primeres ens proporciona un procediment per caracteritzar, en alguns casos, la condici\u00f3 de reversibilitat del centre degenerat. D#altra banda, relacionem  l#exist\u00e9ncia de integrals primeres anal\u00edtiques amb la reversibilitat orbital anal\u00edtica en el cas de singularitats d\u00e9bils no degenerades.  url: http:\/\/hdl.Handle.Net\/10803\/81314<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Discrete and continuous symmetries in planar vector fields<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Discrete and continuous symmetries in planar vector fields <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Susana Maza Sabido <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Lleida<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 05\/12\/2008<\/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>Jaume Gine Mesa<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: jaume Llibre salo <\/li>\n<li>florina-adriana Buica (vocal)<\/li>\n<li>antoni Guillam\u00f3n grabolosa (vocal)<\/li>\n<li>v\u00edctor Ma\u00f1osa fernandez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Susana Maza Sabido Aquesta tesi es situa en el marc de la teoria qualitativa dels sistemes d#equacions [&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":[26590,12585,18842],"tags":[117114,150371,88273,25416,150370,107289],"class_list":["post-68488","post","type-post","status-publish","format-standard","hentry","category-algebra-de-lie","category-ecuaciones-diferenciales-ordinarias","category-lleida","tag-antoni-guillamon-grabolosa","tag-florina-adriana-buica","tag-jaume-gine-mesa","tag-jaume-llibre-salo","tag-susana-maza-sabido","tag-victor-manosa-fernandez"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/68488","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=68488"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/68488\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=68488"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=68488"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=68488"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}