shadowing lemma

Let M be a Riemannian manifoldMathworldPlanetmath, f:MM a diffeomorphismMathworldPlanetmath and ΛM a compactPlanetmathPlanetmath hyperbolic set for f. Then there is a neighborhood U of Λ such that for every δ>0 there is an ϵ>0 so that every ϵ-orbit ( in U is δ-shadowed by an orbit of f.

Moreover, there is δ0>0 such that, if δ<δ0 and if the pseudo-orbit is bi-infinite, then the shadowing orbit is unique; and if Λ has a local product structure then the shadowing orbit is in Λ.

Title shadowing lemma
Canonical name ShadowingLemma
Date of creation 2013-03-22 14:07:22
Last modified on 2013-03-22 14:07:22
Owner Koro (127)
Last modified by Koro (127)
Numerical id 6
Author Koro (127)
Entry type Theorem
Classification msc 37C50