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Ergodic Theory Seminar - Kecheng Li

Ohio State Garden of Constants
October 15, 2025
12:30 pm - 1:30 pm
Math Tower (MW) 154

231 W 18th Ave, Columbus, OH 43210

Kecheng Li
Tufts University

Title
Unique equilibrium states for Viana maps with small potentials

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. By applying general techniques developed by Climenhaga and Thompson, we show that for every Hölder potential whose oscillation is below an explicit threshold, an equilibrium state not only exists but is unique. All of these conclusions persist under sufficiently small perturbations of the reference map.

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