冀占江, 张更容, 涂井先. 群作用下逆极限空间和乘积空间中的强G-跟踪性[J]. 华南师范大学学报(自然科学版), 2019, 51(6): 103-106. doi: 10.6054/j.jscnun.2019108
引用本文: 冀占江, 张更容, 涂井先. 群作用下逆极限空间和乘积空间中的强G-跟踪性[J]. 华南师范大学学报(自然科学版), 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
Citation: 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

群作用下逆极限空间和乘积空间中的强G-跟踪性

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

  • 摘要: 给出了拓扑群作用下度量空间中强G-跟踪性的概念,研究了拓扑群作用下逆极限空间和乘积空间中强G-跟踪性的动力学性质,得到如下结论: (1)若(Xf, G, d, σ)是系统(X, G, d, f)的逆极限空间,则f具有强G-跟踪性当且仅当σ具有强-跟踪性;(2)f1×f2具有强G-跟踪性当且仅当f1具有强G1-跟踪性,f2具有强G2-跟踪性.这些结论弥补了拓扑群作用下逆极限空间和乘积空间中强G-跟踪性理论的缺失.

     

    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 (Xf, 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.

     

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