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WEAKLY ALMOST PERIODIC POINTS AND CHAOTIC DYNAMICS OF DISCRETE AMENABLE GROUP ACTIONS

Ling, Bin;Nie, Xiaoxiao;Yin, Jiandong

  • Received : 2018.01.08
  • Accepted : 2018.05.11
  • Published : 2019.01.01

Abstract

The aim of this paper is to introduce the notions of (quasi) weakly almost periodic point, measure center and minimal center of attraction of amenable group actions, explore the connections of levels of the orbit's topological structure of (quasi) weakly almost periodic points and study chaotic dynamics of transitive systems with full measure centers. Actually, we showed that weakly almost periodic points and quasiweakly almost periodic points have distinct orbit's topological structure and proved that there exists at least countable Li-Yorke pairs if the system contains a proper (quasi) weakly almost periodic point and that a transitive but not minimal system with a full measure center is strongly ergodically chaotic.

Keywords

weakly almost periodic points;measure centers;amenable group actions;chaotic dynamics

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Acknowledgement

Supported by : National Natural Science Foundation of China