SRB Measures for Polygonal Billiards with Contracting Reflection Laws

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.

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Correspondence to João Lopes Dias.

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Communicated by M. Lyubich

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Del Magno, G., Lopes Dias, J., Duarte, P. et al. SRB Measures for Polygonal Billiards with Contracting Reflection Laws. Commun. Math. Phys. 329, 687–723 (2014). https://doi.org/10.1007/s00220-014-1960-x

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Keywords

  • Periodic Point
  • Regular Polygon
  • Parallel Side
  • Hyperbolic Attractor
  • Billiard Trajectory