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JI Zhanjiang, LIU Hailin. The Research of G-lipschitz Shadowing Property, G-equicontinuity and G-non-wandering Point Set[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(4): 111-115. DOI: 10.6054/j.jscnun.2024056
Citation: JI Zhanjiang, LIU Hailin. The Research of G-lipschitz Shadowing Property, G-equicontinuity and G-non-wandering Point Set[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(4): 111-115. DOI: 10.6054/j.jscnun.2024056

The Research of G-lipschitz Shadowing Property, G-equicontinuity and G-non-wandering Point Set

  • By using the properties between the map f in metric G-space and induced map \hatf in orbital space, the dynamical relationship between G-Lipschitz shadowing property, G-equicontinuity, G-non-wandering point of the map f and Lipschitz shadowing property, equicontinuity, non-wandering point of the induced map \hatf are studied. The following conclusions are obtained: (1)The map f has G-Lipschitz shadowing property if and only if the induced map \hatf has Lipschitz shadowing property. (2)The map f is G-equicontinuous if and only if the induced map \hatf is equicontinuous. (3)The G-non-wandering point set ΩG(f) of the map f is dense in X if and only if the non-wandering point set Ω(\hatf) of the induced map \hatf is dense in X/G.
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