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Indecomposability and Devaney’s chaoticity of semiflows with an arbitrary acting abelian topological semigroup

Indecomposability and Devaney’s chaoticity of semiflows with an arbitrary acting abelian... We prove that a semiflow with an arbitrary acting abelian topological semigroup is Devaney chaotic if and only if it is nonminimal, indecomposable and has a dense set of periodic points. This generalizes a result of X. Wang and Y. Huang. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Semigroup Forum Springer Journals

Indecomposability and Devaney’s chaoticity of semiflows with an arbitrary acting abelian topological semigroup

Miller, Alica
Semigroup Forum , Volume 96 (3) – Jun 21, 2017
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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algebra
ISSN
0037-1912
eISSN
1432-2137
DOI
10.1007/s00233-017-9881-6
Publisher site
See Article on Publisher Site

Abstract

We prove that a semiflow with an arbitrary acting abelian topological semigroup is Devaney chaotic if and only if it is nonminimal, indecomposable and has a dense set of periodic points. This generalizes a result of X. Wang and Y. Huang.

Journal

Semigroup Forum – Springer Journals

Published: Jun 21, 2017

References

  • On Devaney’s definition of chaos
    Banks, J; Brooks, J; Cairns, G; Davis, G; Stacey, P
  • An Introduction to Chaotic Dynamical Systems
    Devaney, RL
  • On various conditions that imply sensitivity of monoid actions
    Miller, A
  • Syndetic sensitivity in semiflows
    Miller, A; Money, C
  • Devaney’s chaos revisited
    Wang, X; Huang, Y