University of Ostrava, Czech Republic
Date(s) : 31/05/2022 iCal
11 h 00 min - 12 h 00 min
Bunimovich stadium is a convex planar domain whose boundary consists of two semicircles joined by two parallel segments. The billiard map describes the free motion of a point particle in the interior of the stadium with elastic collisions when the particle reaches the boundary. In this talk I will first review some results concerning the estimates of topological entropy of the Bunimovich stadium billiard map, concentrating mainly on the recent result of Misiurewicz and Zhang who provided the lower bound of the topological entropy of Bunimovich stadium billiard map when the length of the parallel sides goes to infinity. Then, I will focus on our work and show how to provide an upper bound of the topological entropy of the Bunimovich stadium billiard map through the use of Cassaigne’s formula. This talk is based on the joint work with Serge Troubetzkoy (Aix-Marseille).