FURTHER STUDIES OF TOPOLOGICAL TRANSITIVITY IN NON-AUTONOMOUS DISCRETE DYNAMICAL SYSTEMS

Jingmin Pi; Tianxiu Lu; Waseem Anwar; Zhiwen Mo

doi:10.11948/20230264

2024 Volume 14 Issue 3

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Jingmin Pi, Tianxiu Lu, Waseem Anwar, Zhiwen Mo. FURTHER STUDIES OF TOPOLOGICAL TRANSITIVITY IN NON-AUTONOMOUS DISCRETE DYNAMICAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1508-1521. doi: 10.11948/20230264

Citation:

Jingmin Pi, Tianxiu Lu, Waseem Anwar, Zhiwen Mo. FURTHER STUDIES OF TOPOLOGICAL TRANSITIVITY IN NON-AUTONOMOUS DISCRETE DYNAMICAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1508-1521. doi: 10.11948/20230264

FURTHER STUDIES OF TOPOLOGICAL TRANSITIVITY IN NON-AUTONOMOUS DISCRETE DYNAMICAL SYSTEMS

1.
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
2.
School of Mathematical Science, Sichuan Normal University, Chengdu 610068, China

Author Bio: Email: pi1011225770@126.com(J. Pi); Email: waseemanwarijt@yahoo.com(W. Anwar); Email: mozhiwen@sicnu.edu.cn(Z. Mo)
Corresponding author: Email: lubeeltx@163.com(T. Lu)
Fund Project: This work was funded by the Project of the Natural Science Foundation of Sichuan Province (Nos. 2023NSFSC0070, 2022NSFSC1821), the Scientific Research and Innovation Team Program of Sichuan University of Science and Engineering (No. SUSE652B002), and the Graduate Student Innovation Fundings (No. y2022189)

Abstract

Abstract

In this paper, notions related to transitivity in autonomous discrete dynamical systems are generalized to non-autonomous discrete dynamical systems. Some sufficient conditions or necessary conditions of transitive were given. Then, it is obtained that the mapping sequence $f_{1, \infty}=(f_{1}, f_{2}, \cdots)$ is $\mathcal{P}$-chaotic if and only if the mapping sequence $f_{n, \infty}=(f_{n}, f_{n+1}, \cdots), \forall n \in \mathbb{N}$ $(\mathbb{N}=\{1, 2, \cdots\})$ would also be $\mathcal{P}$-chaotic. Where $\mathcal{P}$-chaos represents one of the following six properties: transitive, mixing, weakly mixing, syndetically transitive, strongly transitive, and $\mathbb{Z}$-transitive. Finally, an example is given to show that the condition ‘the space has no isolated point’ cannot be removed, and a $\mathcal{P}$-chaotic non-autonomous mapping sequence is provided.
- Non-autonomous discrete dynamical systems /
- transitivity /
- mixing
MSC: 37B40, 37D45, 54H20

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References

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