Title of article
A quantitative approach to syndetic transitivity and topological ergodicity
Author/Authors
Zhao ، Yu - Guangdong Ocean University , Li ، Risong - Guangdong Ocean University , Lu ، Tianxiu - Sichuan University of Science and Engineering , Jiang ، Ru - Guangdong Ocean University , Wang ، Hongqing - Guangdong Ocean University , Liang ، Haihua - Guangdong Ocean University
Pages
7
From page
4680
To page
4686
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.
Keywords
Sensitivity , syndetically sensitive , ergodically sensitive , multi , sensitive , cofinitely sensitive , Furstenberg families
Journal title
Journal of Nonlinear Science and Applications
Serial Year
2017
Journal title
Journal of Nonlinear Science and Applications
Record number
2476835
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