Rafael Ramirez-Ros
Break-up of resonant invariant curves in billiards and dual billiards associated to perturbed circular tables
(227K, Postscript)

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.