Dimension theoretical study on skew product maps with coupled-expanding property

TL;DR

This paper investigates the Hausdorff dimension of attractors in skew product maps with coupled-expanding properties and proves the existence of an ergodic measure with full Hausdorff dimension.

Contribution

It provides a dimension theoretical analysis of skew product maps with coupled-expanding property, including dimension estimates and ergodic measure existence.

Findings

Hausdorff dimension estimates for attractors

Existence of ergodic measure with full Hausdorff dimension

Analysis on skew product maps with coupled-expanding property

Abstract

We discuss on some families of skew product maps on a square. For a kind of skew product maps with coupled-expanding property, we estimate Hausdorff dimension of its attractor. And we prove that there exists an ergodic measure with full Hausdorff dimension for this kind of skew product maps.