Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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WEAKLY ALMOST PERIODIC POINTS AND CHAOTIC DYNAMICS OF DISCRETE AMENABLE GROUP ACTIONS

  • Ling, Bin (Department of Mathematics Nanchang University) ;
  • Nie, Xiaoxiao (Department of Mathematics Nanchang University) ;
  • Yin, Jiandong (Department of Mathematics Nanchang University)
  • Received : 2018.01.08
  • Accepted : 2018.05.11
  • Published : 2019.01.01
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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.

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References

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