000088583 001 __ 88583
000088583 005 __20140605220835.0
000088583 024 8_ $9 driver $a oai:ddd.uab.cat:88583
000088583 035 __ $a oai:www.recercat.cat:2072/182291
000088583 041 __ $a eng
000088583 080 __ $a 53
000088583 100 1_ $a Pinto-de-Carvalho, Sònia
000088583 245 10 $a Nonpersistence of resonant caustics in perturbed elliptic billiards
000088583 260 __ $b Centre de Recerca Matemàtica $c 2011
000088583 300 __ $a 17 p.
000088583 520 __ $a 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.
000088583 540 __ $9 info:eu-repo/semantics/openAccess $a L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: $u http://creativecommons.org/licenses/by-nc-nd/3.0/es/
000088583 546 __ $a Anglès.
000088583 653 __ $a Pertorbació (Matemàtica)
000088583 653 __ $a Òptica geomètrica
000088583 655 _4 $a info:eu-repo/semantics/preprint
000088583 700 1_ $a Ramírez Ros, Rafael
000088583 710 1_ $a Centre de Recerca Matemàtica
000088583 762 18 $w hdl_2072_1177
000088583 830 __ $a Prepublicacions del Centre de Recerca Matemàtica ; $v 1041
000088583 856 40 $p 17 $s 194204 $u http://ddd.uab.cat/pub/prepub/2011/hdl_2072_182291/Pr1041.pdf
000088583 856 42 $3 Adreça alternativa $u http://hdl.handle.net/2072/182291
000088583 980 __ $a PREPUB $b UAB