On the dynamical asymptotic dimension of a free $\mathbb Z^d$-action on the Cantor set

TL;DR

This paper establishes an upper bound on the dynamical asymptotic dimension for extensions of free b^d-actions on the Cantor set, providing insights into their structural complexity.

Contribution

It proves that any extension of a free b^d-action on the Cantor set has dynamical asymptotic dimension at most 3^d - 1, a new universal bound.

Findings

Dynamical asymptotic dimension is bounded by 3^d - 1.

The result applies to arbitrary extensions of free b^d-actions.

Provides a universal upper bound for the complexity of such dynamical systems.

Abstract

Consider an arbitrary extension of a free $\mathbb Z^d$-action on the Cantor set. It is shown that it has dynamical asymptotic dimension at most $3^d - 1$.