Topological Ergodic Shadowing and Chaos on Uniform Spaces

Author:

Wu Xinxing1ORCID,Ma Xin2,Zhu Zhu3,Lu Tianxiu4

Affiliation:

1. School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, P. R. China

2. School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, P. R. China

3. College of Management Science, Chengdu University of Technology, Chengdu, Sichuan 610059, P. R. China

4. School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, P. R. China

Abstract

This paper firstly proves that every dynamical system defined on a Hausdorff uniform space with topologically ergodic shadowing is topologically mixing, thus topologically chain mixing. Then, the following is proved: (1) every weakly mixing dynamical system defined on a second countable Baire–Hausdorff uniform space is chaotic in the sense of both Li–Yorke and Auslander–Yorke; (2) every point transitive dynamical system defined on a Hausdorff uniform space is either almost equicontinuous or sensitive.

Funder

the National Natural Science Foundation of China

scientific research starting project of Southwest Petroleum University

Technology Innovation Team of Southwest Petroleum University for Nonlinear Systems

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

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