FURTHER DISCUSSION ON KATO'S CHAOS IN SET-VALUED DISCRETE SYSTEMS

Risong Li; Tianxiu Lu; Guanrong Chen; Xiaofang Yang

doi:10.11948/20190388

2020 Volume 10 Issue 6

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Risong Li, Tianxiu Lu, Guanrong Chen, Xiaofang Yang. FURTHER DISCUSSION ON KATO'S CHAOS IN SET-VALUED DISCRETE SYSTEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2491-2505. doi: 10.11948/20190388

Citation:

Risong Li, Tianxiu Lu, Guanrong Chen, Xiaofang Yang. FURTHER DISCUSSION ON KATO'S CHAOS IN SET-VALUED DISCRETE SYSTEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2491-2505. doi: 10.11948/20190388

FURTHER DISCUSSION ON KATO'S CHAOS IN SET-VALUED DISCRETE SYSTEMS

1.
School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, 524025, China
2.
School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, China
3.
Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, 999077, China
4.
Artificial Intelligence Key Laboratory of Sichuan Province, Bridge Nondestruction Detecting and Engineering Computing Key Laboratory of Sichuan Province, Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong, 643000, China

Corresponding author: Email address: lubeeltx@163.com (T. Lu)
Fund Project: This work was funded by the Opening Project of Artificial Intelligence Key Laboratory of Sichuan Province (2018RZJ03), the Opening Project of Bridge Non-destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province (2018QZJ03), the Opening Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things (2020WZJ01), and the Scientific Research Project of Sichuan University of Science and Engineering (2020RC24)

Abstract

Abstract

For a compact metric space $ Y $ and a continuous map $ g:Y\rightarrow Y $, the collective accessibility and collectively Kato chaotic of the dynamical system $ (Y, g) $ were defined. The relations between topologically weakly mixing and collective accessibility, or strong accessibility, or strongly Kato chaos were studied. Some common properties of $ g $ and $ \overline{g} $ were given. Where $ \overline{g}: \kappa(Y)\rightarrow \kappa(Y) $ is defined as $ \overline{g}(B) = g(B) $ for any $ B\in\kappa(Y) $, and $ \kappa(Y) $ is the collection of all nonempty compact subsets of $ Y $. Moreover, it is proved that $ g $ is collectively accessible (or strongly accessible) if and only if $ \overline{g} $ in $ w^{e} $-topology is collectively accessible (or strongly accessible).
- Kato's chaos /
- collective accessibility /
- strongly accessible
MSC: 37B40, 37D45, 54H20

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References

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