Dia: Dimecres 17 de juny de 2026
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Tere M-Seara (UPC)
Títol: Chaos in generic analytic convex billiards
Resum: In this talk we will show the abundance of Chaos in analytic convex billiards.
It is well known that, for a convex billiard table, the corresponding billiard map is a twist map on the cylinder.
We will proof that such map has hyperbolic periodic orbits whose stable and unstable manifolds intersect transversally, giving rise to the existence of horseshoes and, therefore, to hyperbolic invariant sets whose dynamics is conjugated to the Bernoulli shift.
The abundance of transverse homoclinic orbits has been only proved for generic smooth billiard tables.
The novelty of our work is that, going back to some ideas of Zehnder of 1972, we prove that the set of analytic billiards such that "given any rational rotation number, there is a unique periodic orbit in the associated Aubry-Mather set, whose stable and unstable manifolds intersect and whose intersections are all transversal” form a Baire generic set with the usual analytic topology.
The result is in collaboration with I. Baldomá (U.Politecnica de Catalunya) A. Florio (U. Paris Dauphine) and M. Leguil (E. Polytechnique Paris).
Last updated: Sat Jun 13 16:07:55 2026