The asymptotic average-shadowing property and transitivity for flows

Rongbao Gu

Chaos, Solitons & Fractals, 2009, vol. 41, issue 5, 2234-2240

Abstract: The asymptotic average-shadowing property is introduced for flows and the relationships between this property and transitivity for flows are investigated. It is shown that a flow on a compact metric space is chain transitive if it has positively (or negatively) asymptotic average-shadowing property and a positively (resp. negatively) Lyapunov stable flow is positively (resp. negatively) topologically transitive provided it has positively (resp. negatively) asymptotic average-shadowing property. Furthermore, two conditions for which a flow is a minimal flow are obtained.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:5:p:2234-2240

DOI: 10.1016/j.chaos.2008.08.029

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