- 05-167 Rafael Ramirez-Ros
- Break-up of resonant invariant curves in billiards and dual billiards associated to perturbed circular tables
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.