Transitivity and sensitivity for the $ p $-periodic discrete system via Furstenberg families

Xiaofang Yang; Tianxiu Lu; Waseem Anwar; Xiaofang Yang; Tianxiu Lu; Waseem Anwar

doi:10.3934/math.2022078

AIMS Mathematics

2022, Volume 7, Issue 1: 1321-1332. doi: 10.3934/math.2022078

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Research article

Transitivity and sensitivity for the $ p $-periodic discrete system via Furstenberg families

1.
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
2.
Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong 643000, China
3.
School of Mathematical Science, Sichuan Normal University, Chengdu 610068, China

Received: 25 August 2021 Accepted: 13 October 2021 Published: 22 October 2021
MSC : 37B45, 37B55, 54H20

The consistency and implication relation of chaotic properties of $ p $-periodic discrete system and its induced autonomous discrete system are obtained. The chaotic properties discussed involve several types of transitivity and some stronger forms of sensitivity in the sense of Furstenberg families.
- $ p $-periodic discrete system,
- Furstenberg families,
- transitivity,
- sensitivity,
- mixing
Citation: Xiaofang Yang, Tianxiu Lu, Waseem Anwar. Transitivity and sensitivity for the $ p $-periodic discrete system via Furstenberg families[J]. AIMS Mathematics, 2022, 7(1): 1321-1332. doi: 10.3934/math.2022078

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Abstract

The consistency and implication relation of chaotic properties of $ p $-periodic discrete system and its induced autonomous discrete system are obtained. The chaotic properties discussed involve several types of transitivity and some stronger forms of sensitivity in the sense of Furstenberg families.

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