Leírás
University of Szeged, Bolyai Institute, Differential equations seminar and Stochastics seminar
Abstract. Billiards are dynamical systems that describe the motion of a point particle inside a planar domain. The particle propagates along straight lines within the domain, and has specular reflections at the boundary. These simple systems may exhibit a wide scale of dynamical phenomena depending on the shape of the domain. After some general introduction, I would like to discuss open dispersing billiards obtained by removing three strictly convex scatterers satisfying a non-eclipse condition from the plane. We show that information on the length of all periodic orbits determine the Lyapunov exponents and the curvatures of the scatterers at the base points of period two orbits.
This is joint work with Jacopo de Simoi, Vadim Kaloshin and Martin Leguil.