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Nonpersistence of resonant caustics in perturbed elliptic billiards
Pinto-de-Carvalho, Sònia; Ramírez Ros, Rafael
Centre de Recerca Matemàtica
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.
53 - Física
Pertorbació (Matemàtica)
Òptica geomètrica
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17 p.
Centre de Recerca Matemàtica
Prepublicacions del Centre de Recerca Matemàtica;1041

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