Project CEMAPRE internal
| Title | Billiards in polytopes |
| Participants | Gianluigi Del Magno (Principal Investigator), Pedro Duarte, José Pedro Gaivão, João Lopes Dias |
| Summary | Hyperbolic 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. |