Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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TWO NEW RECURRENT LEVELS AND CHAOTIC DYNAMICS OF ℤd+-ACTIONS

  • Received : 2022.04.27
  • Accepted : 2022.07.11
  • Published : 2022.11.01
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Abstract

In this paper, we introduce the concepts of (quasi-)weakly almost periodic point and minimal center of attraction for ℤd+-actions, explore the connections of levels of the topological structure the orbits of (quasi-)weakly almost periodic points and discuss the relations between (quasi-)weakly almost periodic point and minimal center of attraction. Especially, we investigate the chaotic dynamics near or inside the minimal center of attraction of a point in the cases of S-generic setting and non S-generic setting, respectively. Actually, we show that weakly almost periodic points and quasi-weakly almost periodic points have distinct topological structures of the orbits and we prove that if the minimal center of attraction of a point is non S-generic, then there exist certain Li-Yorke chaotic properties inside the involved minimal center of attraction and sensitivity near the involved minimal center of attraction; if the minimal center of attraction of a point is S-generic, then there exist stronger Li-Yorke chaotic (Auslander-Yorke chaotic) dynamics and sensitivity (ℵ0-sensitivity) in the involved minimal center of attraction.

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Acknowledgement

This work was financially supported by the National Natural Science Foundation of China (No. 12061043, 11661054).

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