Sala Conferenze (Puteano, Centro De Giorgi).
The dynamics of billiards has been studied in great detail when the reflection law is the specular one, i.e., when the angle of reflection equals the angle of incidence. In this talk, I will be concerned with polygonal billiards with a contracting reflection law, a non-specular reflection law such that the function describing the dependence of the angle of reflection on the angle of incidence is a contraction. The dynamics of polygonal billiards with a contracting reflection law differs greatly from the dynamics of polygonal billiards with the specular reflection law. Whereas the latter are never hyperbolic, genericpolygonal billiards with a contracting reflection lawhave uniformly hyperbolic sets supporting finitely many distinct physical measures. In this talk, I will survey the main the results on polygonal billiards with a contracting reflection law obtained jointly with P. Duarte, J. Lopes Diaz, J. P. Gaivão and D. Pinheiro.