, Volume 84, Issue 1, pp 81-90
Date: 08 Sep 2011

Sensitivity and chaos of semigroup actions

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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.

Communicated by Jimmie D. Lawson.