September 30, 2025Open Access

Exponential mixing of measures of maximal entropy for certain skew products

Key Points

The study reveals a connection between fiber entropy and Lyapunov exponents for skew products with 2-dimensional fibers.
Research extends previous theorems, showing new classes of skew products exhibiting strong positive recurrence.
These skew products have a finite number of measures of maximal entropy, all exhibiting exponential mixing.
Statistical properties indicate good behavior in the context of dynamical systems and entropy.

Abstract

We establish a relation between the continuity of the fiber entropy and the continuity of the fiber Lyapunov exponents for skew products with 2-dimensional fibers. This result extends the theorem for surfaces proved by Buzzi-Crovisier-Sarig. As a consequence, we are able to obtain classes of skew products that satisfies the strong positive recurrence (SPR) property, in particular it has finite number of measures of maximal entropy, all exponentially mixing with good statistical properties.

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