Chaotic Actions of Locally Compact Hausdorff Topological Groups | Zendy

Friedrich Martin Schneider | Zendy

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Chaotic Actions of Locally Compact Hausdorff Topological Groups

Author(s) -

Friedrich Martin Schneider

Publication year - 2014

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2014.02.009

Subject(s) - mathematics , locally compact space , hausdorff space , group action , generalization , pure mathematics , group (periodic table) , topological space , class (philosophy) , topological group , topology (electrical circuits) , locally compact group , chaotic , homeomorphism (graph theory) , action (physics) , discrete mathematics , mathematical analysis , combinatorics , computer science , artificial intelligence , chemistry , organic chemistry , physics , quantum mechanics

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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