The Strong <i>G</i>-shadowing Property of the Inverse Limit Spaces and the Product Spaces of Group Action

JI Zhanjiang; ZHANG Gengrong; TU Jingxian

doi:10.6054/j.jscnun.2019108

Journal of South China Normal University (Natural Science Edition) > 2019 > 51(6): 103-106. > DOI: 10.6054/j.jscnun.2019108

JI Zhanjiang, ZHANG Gengrong, TU Jingxian. The Strong G-shadowing Property of the Inverse Limit Spaces and the Product Spaces of Group Action[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(6): 103-106. DOI: 10.6054/j.jscnun.2019108

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The Strong G-shadowing Property of the Inverse Limit Spaces and the Product Spaces of Group Action

1.
School of Data Science and Software Engineering//Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System, Wuzhou University, Wuzhou 543002, China
2.
School of Mathematics and Computational Science, Hunan First Normal University, Changsha 410205, China

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Received Date: January 01, 2019
Available Online: March 21, 2021

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Abstract

Abstract

The concept of the strong G-shadowing property is given in the metric spaces under the action of topologi-cal group. Then the dynamical properties of the strong G-shadowing property in the inverse limit spaces and the product spaces under the action of topological group are studied. The following conclusions are obtained. Let the system (X_f, G, d, σ) be the inverse limit spaces of the system (X, G, d, f). Then f has the G-shadowing property if and only if σ has the G-shadowing property. The product map f₁×f₂ has the strong G-shadowing property if and only if the map f₁ has the strong G₁-shadowing property and the map f₂ has the strong G₂-shadowing property. These results enrich the theory of strong G-shadowing property in the inverse limit spaces and the product spaces under the action of topological group.
- G-shadowing property,
- strong G-shadowing property,
- inverse limit spaces,
- product spaces

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