Geodesic
A quantitative approach to syndetic transitivity and topological ergodicity
Zhao, Yu 1 ; Li, Risong 1 ; Lu, Tianxiu 2 ; Jiang, Ru 1 ; Wang, Hongqing 1 ; Liang, Haihua 1
1 School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People's Republic of China
2 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
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 9, p. 4680-4686.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.09.10
Classification : 37B10, 37C20, 37C50
Keywords: Sensitivity, syndetically sensitive, ergodically sensitive, multi-sensitive, cofinitely sensitive, Furstenberg families.

Zhao, Yu  1 ; Li, Risong  1 ; Lu, Tianxiu  2 ; Jiang, Ru  1 ; Wang, Hongqing  1 ; Liang, Haihua  1

1 School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People's Republic of China
2 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 
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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 its applications, Tome 10 (2017) no. 9, p. 4680-4686. doi : 10.22436/jnsa.010.09.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.09.10/

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