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Unique equilibrium states for Viana maps for small potentials
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems , First View
- Published online by Cambridge University Press:
- 03 March 2026, pp. 1-20
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- Article
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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.
