Title:
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Nonpersistence of resonant caustics in perturbed elliptic billiards
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Author:
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Pinto-de-Carvalho, Sònia; Ramírez Ros, Rafael; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
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Abstract:
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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. |
Subject(s):
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-Pertorbació (Matemàtica) -Òptica geomètrica |
Rights:
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open access
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:
https://creativecommons.org/licenses/by-nc-nd/3.0/ |
Document type:
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Article Prepublicació |
Published by:
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Centre de Recerca Matemàtica
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Share:
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Uri:
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https://ddd.uab.cat/record/88583
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