Lipschitz Shadowing for Flows

Kennet J. Palmer; Sergei Pilyugin; Sergey Tikhomirov

Lipschitz Shadowing for Flows

Dynamical Systems 2011-03-17 v1

Authors: Kennet J. Palmer , Sergei Pilyugin , Sergey Tikhomirov

Abstract

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 $X$ .

Keywords

shadowing property geodesic flow

Cite

@article{arxiv.1103.3210,
  title  = {Lipschitz Shadowing for Flows},
  author = {Kennet J. Palmer and Sergei Pilyugin and Sergey Tikhomirov},
  journal= {arXiv preprint arXiv:1103.3210},
  year   = {2011}
}

Comments

35 pages

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