关于平均跟踪性质与渐近平均跟踪性质的两点注记  

Two Notes on The Average Shadowing Property and The Asymptotic Average Shadowing Property

作　　者：牛应轩[1] 

机构地区：[1]皖西学院数理系,安徽六安237012

出　　处：《皖西学院学报》2008年第5期1-3,共3页Journal of West Anhui University

基　　金：安徽省教育厅自然科学研究项目(KJ2007B123)

摘　　要：在动力系统的稳定性和混沌的研究中,引入了各种跟踪性质的概念。讨论了平均跟踪性质与渐近平均跟踪性质,证明了如果X是至少包含两点的紧致度量空间,iXX→X为恒同映射,则iX没有平均跟踪性质和渐近平均跟踪性质。此结果改进了两个已知结论。Various shadowing properties are introduced for the research on the chaos and the stability of dynamical systems. In this note, we discuss the average shadowing property and the asymptotic average shadowing property, it is shown that if ix ：X→X is the identity map where X is a compact metric space with at least two points, then ix does not has the average shadowing property and the asymptotic average shadowing property. Two known conclusions are generalized by the result.

关 键 词：伪轨跟踪性质 平均跟踪性质 渐近平均跟踪性质 完全不连通. 

分 类 号：O189.1[理学—数学]