A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property | Zendy

Risong Li | Zendy; Xiaoliang Zhou | Zendy

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A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property

Author(s) -

Risong Li,

Xiaoliang Zhou

Publication year - 2011

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2011/360583

Subject(s) - ergodicity , mathematics , metric space , property (philosophy) , metric (unit) , transitive relation , pure mathematics , space (punctuation) , locally compact space , lyapunov function , mathematical analysis , combinatorics , computer science , physics , statistics , epistemology , philosophy , operations management , nonlinear system , quantum mechanics , economics , operating system

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

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