Exponential mixing of measures of maximal entropy for certain skew products
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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- Ergodic Theory and Dynamical Systems
- Publisher
- Cambridge University Press (CUP)
- Volume
- 46
- Issue
- 10
- Pages
- 2620–2644
- Publication date
- 1 June 2026
- Language
- EN