More on tame dynamical systems

TL;DR

This paper surveys and extends results on tame dynamical systems, providing new examples, characterizations, and conditions, especially focusing on tame symbolic systems and their coding functions.

Contribution

It offers new results, characterizations, and examples of tame dynamical systems, enhancing understanding of their structure and properties.

Findings

Characterization of tame subshifts

Sufficient conditions for tame coding functions

Examples of tame systems in universal Polish group dynamics

Abstract

In this work, on the one hand, we survey and amplify old results concerning tame dynamical systems and, on the other, prove some new results and exhibit new examples of such systems. In particular, we study tame symbolic systems and establish a neat characterization of tame subshifts. We also provide sufficient conditions which ensure that certain coding functions are tame. Finally we discuss examples where certain universal dynamical systems associated with some Polish groups are tame.