Abstract
We derive equations for invariant distributions of billiards as invertible (measure-preserving) dynamic systems in a symmetric phase space and find their solutions. We introduce and investigate invariant measures for the complete and contracted descriptions and establish the relation between them.
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Naydenov, S.V., Yanovsky, V.V. Invariant Distributions in Systems with Elastic Reflections. Theoretical and Mathematical Physics 130, 256–270 (2002). https://doi.org/10.1023/A:1014295517366
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DOI: https://doi.org/10.1023/A:1014295517366