Uniformly rigid models for rigid actions

TL;DR

This paper demonstrates that any ergodic rigid system can be represented by a topologically uniformly rigid and weak mixing dynamical system, bridging ergodic theory and topological dynamics.

Contribution

It introduces a method to realize ergodic rigid systems as uniformly rigid, weakly mixing topological dynamical systems, expanding the understanding of their topological models.

Findings

Any ergodic rigid system can be topologically realized as a uniformly rigid, weak mixing system.

The realization preserves ergodic and rigidity properties in the topological setting.

Provides a new connection between ergodic theory and topological dynamics.

Abstract

In this article we show that any ergodic rigid system can be topologically realized by a uniformly rigid and (topologically) weak mixing topological dynamical system.