On the Entropy Points and Shadowing in Uniform Spaces

Author:

Ahmadi Seyyed Alireza1,Wu Xinxing23ORCID,Feng Zonghong2,Ma Xin4,Lu Tianxiu5

Affiliation:

1. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

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

3. Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China

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

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

Abstract

We introduce and study the topological concepts of entropy points, expansivity and shadowing property for dynamical systems on noncompact nonmetrizable spaces, which generalize the relevant concepts for metric spaces. We also obtain various properties on uniform entropy on noncompact nonmetrizable spaces. The main result is a theorem which yields a relation between topological shadowing property and positive uniform entropy.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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