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

Sensitivity and chaos of semigroup actions

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.