Semigroup Forum

, Volume 84, Issue 1, pp 81–90

Sensitivity and chaos of semigroup actions

RESEARCH ARTICLE

DOI: 10.1007/s00233-011-9335-5

Cite this article as:
Wang, H., Long, X. & Fu, H. Semigroup Forum (2012) 84: 81. doi:10.1007/s00233-011-9335-5

Abstract

We prove that if an action of a C-semigroup S on a Polish space is syndetic transitive, then the system is either minimal and equicontinuous, or sensitive. Additionally, we show that if an action of an abelian monoid S on a Polish space has a transitive point x and a periodic orbit O such that \(\overline{Hx}\) is perfect where H={sS:s|O is an identity map}, then the system is chaotic.

Keywords

Semigroup action Sensitivity Chaos Transitive point Equicontinuous 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsGuangzhou UniversityGuangzhouPeople’s Republic of China
  2. 2.College of Mathematics and Information SciencesZhaoqing UniversityZhaoqingPeople’s Republic of China

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