{"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":"Resolution Barcelona Dynamical System Prize 2019"},"content":{"rendered":"

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

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

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

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

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

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

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

works until January 31, 2019<\/p>\n

Award ceremony<\/em><\/span><\/h4>\n

Date
\n<\/strong><\/span>will be announced\u00a0<\/em><\/p>\n

Place
\n<\/strong><\/span>Institute of Catalan Studies<\/p>\n

Place
\n<\/strong><\/span>Institute of Catalan Studies<\/p>\n

Resolution of the Barcelona Dynamical Systems Prize 2019 under the patronage of Professor Carles Sim\u00f3 i Torres<\/strong><\/h2>\n

In this article, the authors prove that the boundary of a strictly convex integrable billiard table sufficiently close to an ellipse or a circle is necessarily an ellipse or a circle. This is a perturbative version of the Birkhoff conjecture, which is commonly considered one of the oldest (and most impenetrable) problems in dynamical systems. To prove this result, the authors introduce a notion of integrability called \u00bbrational integrability\u00bb (the existence of caustics of all periods 1\/q near the boundary of the domain), and show that for these caustics to be preserved under a perturbation of an elliptic domain, a family of subharmonic Melnikov integrals must be identically zero. After a technically demanding analysis of this class of perturbations, they show that the only integrable deformations of an elliptic motion (i.e., those preserving the class of ellipses), thus completing the proof of their main result.<\/p>\n

Link to the resolution.<\/a><\/p>\n

Committee<\/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, Secretary of the jury without vote<\/em><\/p>","protected":false},"excerpt":{"rendered":"

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