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arXiv · 1103.3210

Lipschitz Shadowing for Flows

Kennet J. Palmer·Sergei Pilyugin·Sergey Tikhomirov
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Abstract

Let $ϕ$ be the flow generated by a smooth vector field $X$ on a smooth closed manifold. We show that the Lipschitz shadowing property of $ϕ$ is equivalent to the structural stability of $X$ and that the Lipschitz periodic shadowing property of $ϕ$ is equivalent to the $Ω$-stability of $X$.

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Kennet J. Palmer, Sergei Pilyugin, Sergey Tikhomirov. 2011-03-16. Lipschitz Shadowing for Flows. https://arxiv.org/abs/1103.3210

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