Unique equilibrium states for Viana maps with small potentials
Dynamical Systems
2026-03-05 v1
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 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.
Cite
@article{arxiv.2508.00136,
title = {Unique equilibrium states for Viana maps with small potentials},
author = {Kecheng Li},
journal= {arXiv preprint arXiv:2508.00136},
year = {2026}
}