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Unique equilibrium states for Viana maps for small potentials

Part of: Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  03 March 2026

KECHENG LI
KECHENG LI*
Affiliation:
Department of Mathematics, Tufts University , USA
*
e-mail: kecheng.li@tufts.edu
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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 $\varphi $ 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.

Keywords

equilibrium statespressure gaporbit decomposition

MSC classification

Primary: 37D35: Thermodynamic formalism, variational principles, equilibrium states
Secondary: 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 20
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Copyright
© The Author(s), 2026. Published by Cambridge University Press

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