Lipschitz Shadowing for Flows

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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