Unique equilibrium states for Viana maps for small potentials
Abstract
Abstract We investigate the thermodynamic formalism for Viana maps—skew products obtained by coupling an expanding circle map with a slightly perturbed quadratic family on the fibers. For every Hölder potential phi $\varphi $ φ whose oscillation is below an explicit threshold, we show that an equilibrium state not only exists, but is unique and satisfies an upper level-2 large-deviation principle. All of these conclusions persist under sufficiently small perturbations of the reference map.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Quantum chaos and dynamical systems
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Ergodic Theory and Dynamical Systems
- Volume
- 46
- Issue
- 7
- Pages
- 1819–1838
- Publication date
- 3 March 2026
- Language
- EN