Spatial structure of Sinai-Ruelle-Bowen measures
N. Chernov, A. Korepanov
TL;DR
This paper proves that Sinai-Ruelle-Bowen measures in billiard systems are singular but have absolutely continuous marginal distributions, extending previous observations with rigorous mathematical proofs.
Contribution
It provides a comprehensive mathematical proof that Sinai-Ruelle-Bowen measures are singular yet have absolutely continuous marginals in billiard systems.
Findings
Sinai-Ruelle-Bowen measures are singular in billiard systems.
Marginal distributions of spatial and angular coordinates are absolutely continuous.
The paper generalizes previous observations with full mathematical proofs.
Abstract
Sinai-Ruelle-Bowen measures are the only physically observable invariant measures for billiard dynamical systems under small perturbations. These measures are singular, but as it was observed, marginal distributions of spatial and angular coordinates are absolutely continuous. We generalize these facts and provide full mathematical proofs.
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