Lipschitz Shadowing for Flows

Kennet J. Palmer, Sergei Pilyugin, Sergey Tikhomirov

Published 2011-03-16Version 1

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