Institute of Mathematics


Modul:   MAT760  Ergodic theory and dynamical systems seminar

Birkhoff attractor of dissipative billiards

Talk by Prof. Dr. Anna Florio

Speaker invited by: Prof. Dr. Artur Avila

Date: 13.03.24  Time: 14.45 - 15.45  Room: ETH HG G 19.1

In a joint work with Olga Bernardi and Martin Leguil, we study the dynamics of dissipative convex billiards. In these billiards, the usual elastic reflection law is replaced with a new law where the angle bends towards the normal after each collision. For such billiard dynamics there exists a global attractor; we are interested in the topological and dynamical complexity of an invariant subset of this attractor, the so-called Birkhoff attractor, whose study goes back to Birkhoff, Charpentier, and, more recently, Le Calvez. We show that for a generic convex table, on one hand, the Birkhoff attractor is simple, i.e., a normally contracted submanifold, when the dissipation is strong; while, on the other hand, the Birkhoff attractor is topologically complicated and presents a rich dynamics when the dissipation is mild.