Ergodic properties of families of H\'enon maps

TL;DR

This paper investigates the ergodic properties of families of Hénon maps and their associated random dynamical systems, providing insights into their behavior and entropy characteristics.

Contribution

It introduces a framework for analyzing the ergodic properties of continuous families of Hénon maps and applies it to estimate entropy in skew product systems.

Findings

Established ergodic properties for families of Hénon maps.

Derived lower bounds for entropy of skew product systems.

Enhanced understanding of random dynamical systems generated by Hénon 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.