Samuel Senti (IMPA, Rio de Janeiro, Brazil)

Measures of maximal entropy for a class of non-uniformly hyperbolic 2-dimensional maps.

Abstract. We study perturbations of the skew-product on $S^1\times\mathbb{R}$ given by

$$f(x, y)=(16x, a+\epsilon\sin(2\pi x)-y^2)$$

for some small $\epsilon>0$ and a parameter $a$ for which $y=0$ is preperiodic for the map $a-y^2$ . We show how to prove the existence of equilibrium measures for potentials with small variations including constant potentials.