Lipschitz Shadowing for Flows

Abstract

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

35 pages

References in corpus (2)

• Periodic shadowing and $\Omega$-stability
• Vector Fields with the Oriented Shadowing Property