88583 driver oai:ddd.uab.cat:88583 hdl_2072_1177 oai:www.recercat.cat:2072/182291 eng 53 Pinto-de-Carvalho, Sònia Nonpersistence of resonant caustics in perturbed elliptic billiards Centre de Recerca Matemàtica 2011 17 p. Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard table is an ellipse, any nonsingular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics —the ones whose tangent trajectories are closed polygons— are destroyed under generic perturbations of the billiard table. We prove that none of the resonant elliptical caustics persists under a large class of explicit perturbations of the original ellipse. This result follows from a standard Melnikov argument and the analysis of the complex singularities of certain elliptic functions. info:eu-repo/semantics/openAccess L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Pertorbació (Matemàtica) Òptica geomètrica info:eu-repo/semantics/preprint Ramírez Ros, Rafael Centre de Recerca Matemàtica Prepublicacions del Centre de Recerca Matemàtica ; 1041 17 194204 http://ddd.uab.cat/pub/prepub/2011/hdl_2072_182291/Pr1041.pdf Adreça alternativa http://hdl.handle.net/2072/182291 PREPUB UAB file 0 MD5 397836045eaad156d67f8038ae980174 194204 PDF 1.4 filepath pub/prepub/2011/hdl_2072_182291/Pr1041.pdf disk