The Dynamical Property of <i>G</i>-Strong Chain Recurrent Point Set in Metric <i>G</i>-space

JI Zhanjiang

doi:10.6054/j.jscnun.2022034

Journal of South China Normal University (Natural Science Edition) > 2022 > 54(2): 115-119. > DOI: 10.6054/j.jscnun.2022034

JI Zhanjiang. The Dynamical Property of G-Strong Chain Recurrent Point Set in Metric G-space[J]. Journal of South China Normal University (Natural Science Edition), 2022, 54(2): 115-119. DOI: 10.6054/j.jscnun.2022034

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The Dynamical Property of G-Strong Chain Recurrent Point Set in Metric G-space

JI Zhanjiang^,

School of Data Science and Software Engineering/Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System/Guangxi Colleges and Universities Key Laboratory of Professional Software Technology, Wuzhou University, Wuzhou 543002, China

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Received Date: April 23, 2021
Available Online: May 11, 2022

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Abstract

The topological structure and characteristics of G-strong chain regression point set are studied in the metric space under topological group action and some conclusions of G-strong chain regression point set are obtained: (1) Let (X, d) be a compact metric G-space, G be a compact topological group, and f: X→X be a continuous map; then the set SCR_G(f) is a closed set; (2) Let (X, d) be a compact metric G-space, G be a compact topological group, and f: X→X be an homeomorphic pseudoequivalent map; then f(SCR_G(f))=SCR_G(f); (3) Let(X, d)be a compact metric G-space, f: X→X be an homeomorphic pseudoequivalent map and the metric d be invariant to group G; then SCR_G(f)=SCR_G(f^-1).
- metric G-space,
- pseudo equivalent map,
- G-strong chain recurrent point

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