Chaotic actions of locally compact Hausdorff topological groups
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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 language | English |
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Pages (from-to) | 181-195 |
Number of pages | 15 |
Journal | Electronic Notes in Theoretical Computer Science |
Volume | 303 |
Publication status | Published - 28 Mar 2014 |
Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- chaos, continuous group action, periodicity, topological dynamics, topological group