SRB Measures for Polygonal Billiards with Contracting Reflection Laws

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 poly...

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Veröffentlicht in:	Communications in mathematical physics 2014-07, Vol.329 (2), p.687-723
Hauptverfasser:	Del Magno, Gianluigi, Lopes Dias, João, Duarte, Pedro, Gaivão, José Pedro, Pinheiro, Diogo
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical
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Zusammenfassung:	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.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-014-1960-x