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.
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