A quantitative approach to syndetic transitivity and topological ergodicity
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Authors
Yu Zhao
- School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People's Republic of China.
Risong Li
- School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People's Republic of China.
Tianxiu Lu
- Department of Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, People's Republic of China.
- Artificial Intelligence Key Laboratory of Sichuan Province, Zigong, Sichuan, 643000, People’s Republic of China.
- Bridge Non-destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province, Zigong, Sichuan, 643000, People’s Republic of China.
Ru Jiang
- School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People's Republic of China.
Hongqing Wang
- School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People's Republic of China.
Haihua Liang
- School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People's Republic of China.
Abstract
In this paper, we give new quantitative
characteristics of degrees of syndetical transitivity and
topological ergodicity for a given discrete dynamical system, which
are nonnegative real numbers and are not more than \(1\). For selfmaps
of many compact metric spaces it is proved that a given selfmap is
syndetically transitive if and only if its degree of syndetical
transitivity is \(1\), and that it is topologically ergodic if and
only if its degree of topological ergodicity is one. Moreover, there
exists a selfmap of \([0, 1]\) having all degrees positive.
Share and Cite
ISRP Style
Yu Zhao, Risong Li, Tianxiu Lu, Ru Jiang, Hongqing Wang, Haihua Liang, A quantitative approach to syndetic transitivity and topological ergodicity, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4680--4686
AMA Style
Zhao Yu, Li Risong, Lu Tianxiu, Jiang Ru, Wang Hongqing, Liang Haihua, A quantitative approach to syndetic transitivity and topological ergodicity. J. Nonlinear Sci. Appl. (2017); 10(9):4680--4686
Chicago/Turabian Style
Zhao, Yu, Li, Risong, Lu, Tianxiu, Jiang, Ru, Wang, Hongqing, Liang, Haihua. "A quantitative approach to syndetic transitivity and topological ergodicity." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4680--4686
Keywords
- Sensitivity
- syndetically sensitive
- ergodically sensitive
- multi-sensitive
- cofinitely sensitive
- Furstenberg families.
MSC
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