Chaotic actions of locally compact Hausdorff topological groups

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

In this paper we study continuous actions of topological groups. We introduce a parametrized notion of periodicity - relative to a fixed class of compactifications of the acting group. This yields a natural generalization of Devaney's well-recognized concept of chaos. As our main result, we establish a geometric characterization of those classes of compactifications of a locally compact Hausdorff topological group for which the group admits a faithful chaotic continuous action on some (compact) Hausdorff space.

Details

Original languageEnglish
Pages (from-to)181-195
Number of pages15
JournalElectronic Notes in Theoretical Computer Science
Volume303
Publication statusPublished - 28 Mar 2014
Peer-reviewedYes

Keywords

Keywords

  • chaos, continuous group action, periodicity, topological dynamics, topological group