Ergodic properties of families of H\'enon maps

Abstract

Let $\{H_{\lambda}\}$ be a continuous family of H\'{e}non maps parametrized by $\lambda\in M$, where $M\subset\mathbb C^k$ is compact. The purpose of this paper is to understand some aspects of the random dynamical system obtained by iterating maps from this family. As an application, we study skew products of H\'{e}non maps and obtain lower bounds for their entropy.