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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제59권 제6호
- 발행연도
- 2022.11
- 수록면
- 1,229 - 1,254 (26page)
- DOI
- 10.4134/JKMS.j220202
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초록· 키워드
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In this paper, we introduce the concepts of (quasi-)weakly almost periodic point and minimal center of attraction for $\mathbb{Z}^d_+$-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 ($\aleph_0$-sensitivity) in the involved minimal center of attraction.
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