A note on sensitivity of semigroup actions

Details A note on sensitivity of semigroup actions A note on sensitivity of semigroup actions

2006-07-18

arxiv.org/abs/math/0607440v1

Mathematics

Dynamical Systems

7 pages

Scientific paper

It is well known that for a transitive dynamical system (X,f) sensitivity to initial conditions follows from the assumption that the periodic points are dense. This was done by several authors: Banks, Brooks, Cairns, Davis and Stacey, Silverman, and also by Glasner and Weiss. In the latter article Glasner and Weiss established a stronger result (for compact metric systems) which implies that a transitive non-minimal compact metric system (X,f) with dense set of almost periodic points is sensitive. This is true also for group actions as was proved in a recent book of Glasner. Our aim is to generalize these results in the frame of a unified approach for a wide class of topological semigroup actions including one-parameter semigroup actions on Polish spaces.

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