SRB measures for hyperbolic polygonal billiards
Gianluigi Del Magno, Jo\~ao Lopes Dias, Pedro Duarte, Jos\'e Pedro, Gaiv\~ao, Diogo Pinheiro
TL;DR
This paper demonstrates that certain polygonal billiards with specific reflection laws have hyperbolic attractors with multiple ergodic SRB measures, which are stable under small changes and are common among polygons.
Contribution
It establishes the existence and robustness of hyperbolic attractors with SRB measures in polygonal billiards with contracting reflection laws, a novel result in the field.
Findings
Existence of hyperbolic attractors with SRB measures in polygonal billiards.
SRB measures are robust under small perturbations of the reflection law.
Such billiard tables form a generic set in the space of all polygons.
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 polygons. Specific polygonal tables are studied in detail.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Chaos control and synchronization