Communications in Mathematical Physics

, Volume 329, Issue 2, pp 687–723 | Cite as

SRB Measures for Polygonal Billiards with Contracting Reflection Laws

  • Gianluigi Del Magno
  • João Lopes Dias
  • Pedro Duarte
  • José Pedro Gaivão
  • Diogo Pinheiro
Article

Abstract

We prove that polygonal billiards with contracting reflection laws exhibit hyperbolic attractors with countably many ergodic SRB measures. These measures are robust under small perturbations of the reflection law, and the tables for which they exist form a generic set in the space of all convex polygons. Specific polygonal tables are studied in detail.

Keywords

Periodic Point Regular Polygon Parallel Side Hyperbolic Attractor Billiard Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Gianluigi Del Magno
    • 1
  • João Lopes Dias
    • 2
  • Pedro Duarte
    • 3
  • José Pedro Gaivão
    • 1
  • Diogo Pinheiro
    • 1
  1. 1.CEMAPRE, ISEGUniversidade Técnica de LisboaLisbonPortugal
  2. 2.Departamento de Matemática and CEMAPRE, ISEGUniversidade Técnica de LisboaLisbonPortugal
  3. 3.Departamento de Matemática and CMAF, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal

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