摘要
研究了度量G-空间中G-跟踪性与G-周期跟踪性之间的动力学关系,给出了G-跟踪性和G-周期跟踪性的定义,利用等价映射和伪等价映射的性质,得到:(1)设(X,d)为紧致度量G-空间,G为可交换的紧致群,f:X→X等价,若f具有G-周期跟踪性,则P_(G)(f)=CR_(G)(f)(2);设(X,d)为紧致度量G-空间,G为紧致群,f:X→X等价,若f具有G-跟踪性且P_(G)(f)=W_(G)(f),则f具有G-周期跟踪性;(3)设(X,d)为紧致度量G-空间,G为可交换的紧致群,f:X→X伪等价,若f为G-扩张映射且f具有G-跟踪性,则f具有G-周期跟踪性。所得结论推广了度量空间中跟踪性和周期跟踪性的相关结论。
The dynamical relationship between G-shadowing property and G-periodic shadowing property is studied in metric G-space.The definitions of G-shadowing property and G-periodic shadowing property are given.By using the properties of equivalent mapping and pseudo equivalent mapping,the following results are obtained:(1)let(X,d)be compact metric G-space,G be commutative and compact group and f:X→X be an equivariant map.If f has G-periodic shadowing property,then P_(G)(f)=CR_(G)(f);(2)let(X,d)be compact metric G-space,G be compact group and f:X→X be an equivariant map.If f has G-shadowing property and P_(G)(f)=W_(G)(f),then f has G-periodic shadowing property;(3)let(X,d)be compact metric G-space,G be commutative and compact group and f:X→X be a pseudo equivariant map.If f is G-expansive map and f has G-shadowing property,then f has G-periodic shadowing property.These results generalize the conclusions of shadowing property and periodic shadowing property in metric spaces.
作者
冀占江
JI Zhanjiang(School of Data Science and Software Engineering,Wuzhou University,Wuzhou 543002,Guangxi Zhuang Autonomous Region,China;Guangxi Key Laboratory of Machine Vision and Intelligent Control,Wuzhou University,Wuzhou 543002,Guangxi Zhuang Autonomous Region,China)
出处
《浙江大学学报（理学版）》
CAS
CSCD
北大核心
2023年第4期429-433,共5页
Journal of Zhejiang University（Science Edition）
基金
广西自然科学基金资助项目(2018JJB170034,2020JJA110021)
广西高校中青年教师科研基础能力提升项目(2019KY0681)
梧州学院校级重点项目(2020B007)。
关键词
G-跟踪性
G-周期跟踪性
G-链回归点
G-扩张映射
G-shadowing property
G-periodic shadowing property
G-chain recurrent point
G-expansive map
