Exponential mixing of measures of maximal entropy for certain skew products

2025/09/12 by Karina Marin, Mauricio Poletti, Marin, Karina +4
Mathematics · #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.1017/etds.2026.10314

Abstract

Abstract We establish a relation between the continuity of the fiber entropy and the continuity of the fiber Lyapunov exponents for skew products with two-dimensional fibers. This result extends the theorem for surfaces proved by Buzzi, Crovisier, and Sarig. As a consequence, we are able to obtain classes of skew products that satisfy the strong positive recurrence property, in particular, these maps have finite number of measures of maximal entropy, all exponentially mixing with good statistical properties.

Citations

• Recurrence times and rates of mixing
• Statistical Properties of Dynamical Systems with Some Hyperbolicity

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