A family of chaotic billiards with variable mixing rates

2004/09/12 by N. Chernov, Nikolai Chernov, Chernov, Nikolai +2
Mathematics · Physics and Astronomy · #37A25 #37D50 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #math-ph #math.DS #math.MP #msc:37A25 #msc:37D50

paper · pdf · doi:10.48550/arxiv.math-ph/0409024

23 page, 7 figures

arxiv created 2004/09/12 · openalex publication_date 2004/09/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a one-parameter family of dispersing (hence hyperbolic, ergodic and mixing) billiards where the correlation function of the collision map decays as 1/n^a (here n denotes the discrete time), in which the degree a ∈ (1, ∞) changes continuously with the parameter of the family, β. We also derive an explicit relation between the degree a and the family parameter β.

Citations

• Recurrence times and rates of mixing

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