To cite this record: http://ddd.uab.cat/record/88583
Nonpersistence of resonant caustics in perturbed elliptic billiards
Pinto-de-Carvalho, Sònia
Ramírez Ros, Rafael
Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2011
Description: 17 p.
Series: Prepublicacions del Centre de Recerca Matemàtica ; 1041
Abstract: 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.
Rights: L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: Creative Commons
Language: Anglès.
Document: preprint
Subject: Pertorbació (Matemàtica) ; Òptica geomètrica

Adreça alternativa: http://hdl.handle.net/2072/182291


17 p, 189.7 KB

The record appears in these collections:
Research literature > Preprints

 Record created 2012-03-15, last modified 2014-06-05



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