文章基本信息

标题：A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property
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作者：Risong Li ; Xiaoliang Zhou
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2011
卷号：2011
DOI：10.1155/2011/360583
出版社：Hindawi Publishing Corporation
摘要：We prove that if a continuous, Lyapunov stable map 𝑓 from a compact metric space 𝑋 into itself is topologically transitive and has the asymptotic average shadowing property, then 𝑋 is consisting of one point. As an application, we prove that the identity map 𝑖𝑋∶𝑋→𝑋 does not have the asymptotic average shadowing property, where 𝑋 is a compact metric space with at least two points.