Almost open semigroup actions
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In this paper we prove that if a semigroup is almost open then it is sensitive or there exists a residual set of points of equicontinuity. As a consequence we obtain a sufficient condition for sensitivity that generalizes that given in Kontorovich and Megrelishvili (Semigroup Forum 76:133–141, 2008).
KeywordsSemigroups actions Transitivity Sensitivity
We thank the referee for many useful observations and providing the proofs of the many propositions. We also thank the financial support by the Program MATHAMSUD (France, Chile and Uruguay).
- 1.Akin, E., Auslander, J., Berg, K.: When is a transitive map chaotic? In: Bergelson, V., March, K., Rosenblatt, J. (eds.) Conference in Ergodyc Theory and Probability. de Gruyter, Berlin (1996)Google Scholar
- 3.Glasner, E.: Ergodic theory via joinings. In: Mathematical Surveys and Monographs, vol. 101. American Mathematical Society, Providence (2003)Google Scholar