{"id":12679,"date":"2001-11-09T00:00:00","date_gmt":"2001-11-09T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/curvas-polares-de-una-foliacion-singular\/"},"modified":"2001-11-09T00:00:00","modified_gmt":"2001-11-09T00:00:00","slug":"curvas-polares-de-una-foliacion-singular","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/curvas-polares-de-una-foliacion-singular\/","title":{"rendered":"Curvas polares de una foliaci\u00f3n singular"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Nuria Corral P\u00e9rez <\/strong><\/h2>\n<p>La curva polar representa geom\u00e9tricamente el contacto entre una foliaci\u00f3n y las diferentes foliaciones lineales. La memoria est\u00e1 dedicada al estudio de las propiedades topol\u00f3gicas (o de equisingularidad) minimales de la curva polar gen\u00e9rica en t\u00e9rminos de la reducci\u00f3n de singularidades de la foliaci\u00f3n. Damos una exensi\u00f3n del teorema de descomposici\u00f3n de la polar gen\u00e9rica al caso de foliaciones. Es un resultado de merle cuando se trata de la polar de una curva plana irreducible y de kuo-lu garc\u00eda barroso para una curva con varias ramas. Existen tambi\u00e9n resultados paraciales para el caso de foliaciones (rouill\u00e9).  caracterizamos la clase de foliaciones para las cuales un teorema de descomposici\u00f3n de la polar gen\u00e9rica es cierto: son las foliaciones curva generalizada con modelo logar\u00edtmico no resonante. El modelo loagr\u00edtmico es una manera de represenar globalmente la parte lineal de la holonomia de la foliaci\u00f3n. Demostramos la existencia de modelo logar\u00edtmico para toda curva generalizada dicr\u00edtica o no.  tambi\u00e9n probamos que las curvas generalizadas con modelologar\u00edtmico no resonante tienen la propiedad de alejamiento de las separatrices, lo que completa los resultados de rouill\u00e9. Obtenemos as\u00ed una relaci\u00f3n entre el tipo de singularidad de las separatrices y las componente dicr\u00edticas de la foliaci\u00f3n polar, complementaria de la descripci\u00f3n dada por el teorema de descomposici\u00f3n.  finalmente carcterizamos la topolog\u00eda de una curva polar gen\u00e9rica de una foliaci\u00f3n logar\u00edtmica bajo ciertas condiciones de genericidad. Este resultado se puede exteder a ls foliaciones con modelo logar\u00edtmico gen\u00e9rico.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Curvas polares de una foliaci\u00f3n singular<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Curvas polares de una foliaci\u00f3n singular <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Nuria Corral P\u00e9rez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Valladolid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 11\/09\/2001<\/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>Felipe Cano Torres<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: manuel Aroca jos\u00e9 <\/li>\n<li>bernard Teissier (vocal)<\/li>\n<li>eduardo Casas (vocal)<\/li>\n<li>dominique Cerveau (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Nuria Corral P\u00e9rez La curva polar representa geom\u00e9tricamente el contacto entre una foliaci\u00f3n y las diferentes foliaciones [&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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