{"id":2555,"date":"2020-01-30T09:08:09","date_gmt":"2020-01-30T08:08:09","guid":{"rendered":"https:\/\/scm.iec.cat\/?p=2555"},"modified":"2023-05-15T10:31:20","modified_gmt":"2023-05-15T10:31:20","slug":"resolucio-barcelona-dynamical-system-prize-2019","status":"publish","type":"post","link":"https:\/\/scm.iec.cat\/eng\/resolucio-barcelona-dynamical-system-prize-2019\/","title":{"rendered":"Resoluci\u00f3 Barcelona Dynamical System Prize 2019"},"content":{"rendered":"

Guanyadors<\/em><\/span><\/h4>\n

On the local Birkhoff conjecture for convex billiards<\/i><\/span><\/p>\n

Vadim Kaloshin i Alfonso Sorrentino<\/strong><\/span><\/p>\n

Guanyadors<\/em><\/span><\/h4>\n

On the local Birkhoff conjecture for convex billiards<\/i><\/span><\/p>\n

Vadim Kaloshin i Alfonso Sorrentino<\/strong><\/span><\/p>\n

Per\u00edode<\/em><\/span><\/h4>\n

treballs fins el 31 de gener de 2019<\/p>\n

Entrega de premis<\/em><\/span><\/h4>\n

Data
\n<\/strong><\/span>ser\u00e0 anunciada\u00a0<\/em><\/p>\n

Lloc
\n<\/strong><\/span>Institut d’Estudis Catalans<\/p>\n

Lloc
\n<\/strong><\/span>Institut d’Estudis Catalans<\/p>\n

Resoluci\u00f3 del premi Barcelona Dynamical Systems 2019 sota el mecenatge del professor Carles Sim\u00f3 i Torres<\/strong><\/h2>\n

A aquest article, els autors proven que la frontera d’una taula de billar integrable estrictament convex suficientment a prop d’una el\u00b7lipse o d’un cercle, \u00e9s necess\u00e0riament una el\u00b7lipse o un cercle. Aquesta \u00e9s una versi\u00f3 pertorbativa de la conjectura de Birkhoff, la qual \u00e9s comunament considerada com a un dels m\u00e9s antics (i impenetrable) problema en sistemes din\u00e0mics. A fi de provar aquest resultat, els autors introdueixen una noci\u00f3 d’integrabilitat anomenada \u00bbintegrabilitat racional\u00bb (l’exist\u00e8ncia de c\u00e0ustiques de tots els per\u00edodes 1\/q a prop de la frontera del domini), i demostren que perqu\u00e8 les dites c\u00e0ustiques es preservin per una pertorbaci\u00f3 d’un domini el\u00b7l\u00edptic, una fam\u00edlia d’integrals subharm\u00f2niques de Melnikov han de ser id\u00e8nticament nul\u00b7les. Despr\u00e9s d’una an\u00e0lisi d’aquesta classe de pertorbacions, molt exigent a escala t\u00e8cnica, demostren que les \u00faniques deformacions integrables d’un moviment el\u00b7l\u00edptic (i.e. aquelles que preserven la classe d’el\u00b7lipses), amb el que la prova del seu principal resultat queda completa.<\/p>\n

Enlla\u00e7 a la resoluci\u00f3.<\/a><\/p>\n

Comit\u00e9<\/em><\/span><\/h4>\n

Alain Chenciner
\n<\/strong><\/span>Observatoire de Paris<\/em><\/p>\n

Freddy Dumortier
\n<\/strong><\/span>University of Hasselt<\/em><\/p>\n

Daniel Peralta
\n<\/strong><\/span>ICMAT<\/em><\/p>\n

Amadeu Delshams
\n<\/strong><\/span>UPC, Secretari del jurat sense vot<\/em><\/p>","protected":false},"excerpt":{"rendered":"

Resoluci\u00f3 del premi Barcelona Dynamical Systems 2019 sota el mecenatge del professor Carles Sim\u00f3 i Torres<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,14],"tags":[],"class_list":["post-2555","post","type-post","status-publish","format-standard","hentry","category-barcelona-dynamical-systems","category-premis"],"acf":[],"_links":{"self":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/posts\/2555","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/comments?post=2555"}],"version-history":[{"count":0,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/posts\/2555\/revisions"}],"wp:attachment":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/media?parent=2555"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/categories?post=2555"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/tags?post=2555"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}