G 一链连续点和 G -极限跟踪性

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中图分类号：0189.11 文献标志码：A 文章编号：0253-2395（2025）04-0692-

Abstract： We introduced the concepts of G -chain continuous poin and G -limit shadowing property in metric G space.By using the properties of equivariant map and commutative group， we studied the dynamical properties of G -chain continuous poin and G -limit shadowing property，and obtained the folowing results.（1）The equivalent condition is given for every point tobe G -chain continuous. That is， the map f s G -equicontinuous and has G -shadowing property in metric G space; （2） G -expansivity and G -shadowing property imply G -limit shadowing property.These results enrich the theoryof G -chaincontinuouspoint and G -limit shadowing property in metric G -space.

Key words： G -equicontinuity; G -chain continuous point; G -expansivity; G -limit shadowing property; G -shadowing property

0 引言

等度连续、扩张性和跟踪性是动力系统研究的重点和热点，在动力系统的发展中起着重要的作用，与系统的混沌和复杂性密切相关，很多学者在不同的空间对它们的动力学性质进行了研究，取得了有价值的研究结果[1-14]。（剩余6333字）