dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Pinto-de-Carvalho, Sònia |
dc.contributor.author |
Ramírez Ros, Rafael |
dc.date.accessioned |
2012-03-14T08:07:59Z |
dc.date.available |
2012-03-14T08:07:59Z |
dc.date.created |
2011 |
dc.date.issued |
2011 |
dc.identifier.uri |
http://hdl.handle.net/2072/182291 |
dc.format.extent |
17 p. |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;1041 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.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: http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
Pertorbació (Matemàtica) |
dc.subject.other |
Òptica geomètrica |
dc.title |
Nonpersistence of resonant caustics in perturbed elliptic billiards |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
53 - Física |
dc.embargo.terms |
cap |
dc.description.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. |