Some examples of tame dynamical systems answering questions of Glasner and Megrelishvili

Abstract

Glasner and Megrelishvili proved that every continuous action of a topological group $G$ on a dendrite $X$ is tame. We produce two examples of an action on a dendrite which is not ${\mathrm{tame}}_1$, answering a question they raised. We then show that actions on dendrites have $\beta$-rank at most $2$ and produce examples of tame metric dynamical systems of $\beta$-rank $\alpha$ for any $\alpha <{\omega }_1$, answering another question of Glasner and Megrelishvili.

accepted version

References in corpus (4)

• The structure of tame minimal dynamical systems for general groups
• Group actions on dendrites and curves
• Group actions on treelike compact spaces
• Structural properties of dendrite groups