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

Risong Li and Xiaoliang Zhou

Discrete Dynamics in Nature and Society, 2011, vol. 2011, 1-6

Abstract:

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 i X : X → X does not have the asymptotic average shadowing property, where X is a compact metric space with at least two points.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:360583

DOI: 10.1155/2011/360583

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