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SRB Measures for Polygonal Billiards with Contracting Reflection Laws

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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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Authors and Affiliations

  1. CEMAPRE, ISEG, Universidade Técnica de Lisboa, Rua do Quelhas 6, 1200-781, Lisbon, Portugal

    Gianluigi Del Magno, José Pedro Gaivão & Diogo Pinheiro

  2. Departamento de Matemática and CEMAPRE, ISEG, Universidade Técnica de Lisboa, Rua do Quelhas 6, 1200-781, Lisbon, Portugal

    João Lopes Dias

  3. Departamento de Matemática and CMAF, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C6, Piso 2, 1749-016, Lisbon, Portugal

    Pedro Duarte

Authors
  1. Gianluigi Del Magno
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  2. João Lopes Dias
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  3. Pedro Duarte
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  4. José Pedro Gaivão
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  5. Diogo Pinheiro
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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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  • DOI: https://doi.org/10.1007/s00220-014-1960-x

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