Research projects

Project CEMAPRE internal

TitleBilliards in polytopes
ParticipantsGianluigi Del Magno (Principal Investigator), Pedro Duarte, José Pedro Gaivão, João Lopes Dias
SummaryHyperbolic maps with singularities are models for chaotic systems with non-smooth dynamics such as
mechanical systems with collisions, unilateral contacts and frictions. SRB measures are special
invariant measures that give a detailed description of the statistical properties of a hyperbolic
system. Interesting examples of a hyperbolic maps with singularities are billiards in polygons with
contracting reflection laws. Del Magno, Lopes Dias, Duarte, Gaivão and Pinheiro obtained several
results for these billiards. In particular, we proved that typical billiards in polygons with
contracting reflection laws have exactly finitely many ergodic SRB measures. The main goal of this
part of the project is to extend most of the results we obtain for these billiards to their
counterparts in dimensions greater than two, i.e., to billiards in polytopes with contracting
reflection laws.