G-利普希茨跟踪性、G-等度连续和G-非游荡点集的研究  

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

作　　者：冀占江 刘海林 JI Zhanjiang;LIU Hailin(Applied Mathematics Research Team of the Research Academy of Science/Guangxi Key Laboratory of Machine Vision and Intelligent Control,Wuzhou University,Wuzhou 543002,China;School of Science,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]梧州学院科学研究院应用数学研究团队/广西机器视觉与智能控制重点实验室,梧州543002 [2]江西理工大学理学院,赣州341000

出　　处：《华南师范大学学报（自然科学版）》2024年第4期111-115,共5页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12126415);广西自然科学基金项目(2020JJA110021);梧州学院校级重点项目(2020B007)。

摘　　要：利用度量G-空间中映射f与轨道空间中诱导映射f之间的性质,研究了映射f的G-利普希茨跟踪性、G-等度连续、G-非游荡点与诱导映射f的利普希茨跟踪性、等度连续、非游荡点集之间的动力学关系,得到如下结论:(1)映射f具有G-利普希茨跟踪性■诱导映射f具有利普希茨跟踪性;(2)映射f是G-等度连续的■诱导映射f是等度连续的;(3)映射f的G-非游荡点集ΩG(f)在X中稠密?诱导映射f的非游荡点集Ω(f)在X/G中稠密。By using the properties between the map f in metric G-space and induced map f 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 f are studied.The following conclusions are obtained:(1)The map f has G-Lipschitz shadowing property if and only if the induced map f has Lipschitz shadowing property.(2)The map f is G-equicontinuous if and only if the induced map 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(f) of the induced map f is dense in X/G.

关 键 词：G-利普希茨跟踪性 G-等度连续 G-非游荡点 轨道空间 

分 类 号：O189.11[理学—数学]