Abstract:

This work deals with the abundance of analytic billiards
having chaotic motions. The pioneer work by Zehnder's
on planar twist maps in the 1970's was the first to provide a
methodology for constructing analytic perturbations
of maps in order to obtain transversality between the invariant
manifolds of hyperbolic periodic orbits.
 

In this work, we prove that the set of analytic biliards with negative
curvature having a transversal homoclinic orbit
to periodic orbits of any rational rotation number is generic in the
usual analytic topology. In other words,
we prove that, for analytic biliards, the coexistence of chaotic
dynamics with periodic orbit of any period is prevalent.
We use the Aubrey-Mather theory to face with the transversality of
periodic orbits away from the biliard's table boundary.
 

This is a joint work with Anna Florio,MartinLeguil and Tere M-Seara.