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arXiv · 2508.00136

Unique equilibrium states for Viana maps with small potentials

Kecheng Li
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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 H\"older 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.

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Kecheng Li. 2025-07-31. Unique equilibrium states for Viana maps with small potentials. https://doi.org/10.1017/etds.2026.10290

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