Stretched-exponential mixing for surface semiflows and Anosov flows

2024/06/18 by Daofei Zhang, Zhang, Daofei
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2406.12759

openalex publication_date 2024/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a surface semiflow that is a suspension of a \( C^1+α \) expanding Markov interval map, we prove that, under the assumptions that the roof function is Lipschitz continuous and not cohomologous to a locally constant function, the semiflow exhibits stretched-exponential mixing with respect to the SRB measure. This result extends to hyperbolic skew-product semiflows and hyperbolic attractors. Specifically, codimension-one topologically mixing Anosov flows with Lipschitz continuous stable foliations demonstrate stretched-exponential mixing with respect to their SRB measures.

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