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Yanjie Tang,Jiandong Yin 대한수학회 2020 대한수학회보 Vol.57 No.1
The aim of this paper is to show that for the one-sided symbolic system, there exist an uncountable distributively chaotic set contained in the set of irregularly recurrent points and an uncountable distributively chaotic set in a sequence contained in the set of proper positive upper Banach density recurrent points.
Tang, Yanjie,Yin, Jiandong Korean Mathematical Society 2020 대한수학회보 Vol.57 No.1
The aim of this paper is to show that for the one-sided symbolic system, there exist an uncountable distributively chaotic set contained in the set of irregularly recurrent points and an uncountable distributively chaotic set in a sequence contained in the set of proper positive upper Banach density recurrent points.
FIXED POINT THEOREMS ON GENERALIZED CONE METRIC SPACES OVER BANACH ALGEBRAS AND APPLICATIONS
Leng, Qianqian,Yin, Jiandong Korean Mathematical Society 2018 대한수학회지 Vol.55 No.6
The aim of this paper is to introduce the concept of generalized cone metric spaces over Banach algebras as a generalization of generalized metric spaces and present several fixed point results of a class of contractive mappings in generalized cone metric spaces over Banach algebras. Moreover, in order to support our main results, one example is given at the end of this paper.
Fixed point theorems on generalized cone metric spaces over Banach algebras and applications
Qianqian Leng,Jiandong Yin 대한수학회 2018 대한수학회지 Vol.55 No.6
The aim of this paper is to introduce the concept of generalized cone metric spaces over Banach algebras as a generalization of generalized metric spaces and present several fixed point results of a class of contractive mappings in generalized cone metric spaces over Banach algebras. Moreover, in order to support our main results, one example is given at the end of this paper.
TWO NEW RECURRENT LEVELS AND CHAOTIC DYNAMICS OF ℤ<sup>d</sup><sub>+</sub>-ACTIONS
Xie, Shaoting,Yin, Jiandong Korean Mathematical Society 2022 대한수학회지 Vol.59 No.6
In this paper, we introduce the concepts of (quasi-)weakly almost periodic point and minimal center of attraction for ℤ<sup>d</sup><sub>+</sub>-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 (ℵ<sub>0</sub>-sensitivity) in the involved minimal center of attraction.
WEAKLY ALMOST PERIODIC POINTS AND CHAOTIC DYNAMICS OF DISCRETE AMENABLE GROUP ACTIONS
Ling, Bin,Nie, Xiaoxiao,Yin, Jiandong Korean Mathematical Society 2019 대한수학회지 Vol.56 No.1
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.
Weakly almost periodic points and chaotic dynamics of discrete amenable group actions
Bin Ling,Xiaoxiao Nie,Jiandong Yin 대한수학회 2019 대한수학회지 Vol.56 No.1
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 quasi-weakly 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.