publication . Preprint . 2015

Topological entropy of continuous actions of compactly generated groups

Schneider, Friedrich Martin;
Open Access English
  • Published: 13 Feb 2015
We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact Hausdorff space with vanishing topological entropy is amenable. Given an arbitrary compactly generated locally compact Hausdorff topological group $G$, we consider the canonical action of $G$ on the closed unit ball of $L^{1}(G)' \cong L^{\infty}(G)$ endowed with the corresponding weak-$^{\ast}$ topology. We prove that this action has vanishing topological entropy if and only if $G$ is compact. Furthermore, we show that the consider...
free text keywords: Mathematics - Group Theory, Mathematics - Dynamical Systems, Mathematics - General Topology
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