05-167 Rafael Ramirez-Ros

Break-up of resonant invariant curves in billiards and dual billiards associated to perturbed circular tables (227K, Postscript) May 10, 05

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Abstract. Two area-preserving twist maps are associated to a smooth closed convex table: the (classical) billiard map and the dual billiard map. For circular tables, they are integrable and their phase spaces are foliated by invariant curves. The invariant curves with a rational rotation number are resonant and do not persist under generic perturbations. We present a criterion, obtained by a standard Melnikov approach from classical variational techniques, to distinguish when a given resonant invariant curve of some of these billiard maps does not persist under a concrete perturbation of a circular table.

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