Mean Topological Dimension for random bundle transformations

TL;DR

This paper introduces the concept of mean topological dimension for random bundle transformations and establishes conditions under which it is zero, such as finite topological entropy or the small boundary property.

Contribution

It is the first to define mean topological dimension for random bundle transformations and connect it with existing properties like entropy and boundary conditions.

Findings

Mean topological dimension is zero for systems with finite entropy.

Systems with the small boundary property also have zero mean topological dimension.

Abstract

We introduce the mean topological dimension for random bundle transformations, and show that continuous bundle random dynamical systems with finite topological entropy, or the small boundary property have zero mean topological dimensions.