Holder Shadowing on Finite Intervals

Abstract

For any $\theta ,\omega >1/2$ we prove that, if any $d$-pseudotrajectory of length $\sim 1/d^{\omega }$ of a diffeomorphism $f\in C^2$ can be $d^{\theta }$-shadowed by an exact trajectory, then $f$ is structurally stable. Previously it was conjectured by Hammel-Grebogi-Yorke that for $\theta =\omega =1/2$ this property holds for a wide class of non-uniformly hyperbolic diffeomorphisms. In the proof we introduce the notion of sublinear growth property for inhomogenious linear equations and prove that it implies exponential dichotomy.

19 pages. Minor changes

References in corpus (2)

• Lipschitz shadowing implies structural stability
• Periodic shadowing and $\Omega$-stability

Cited by in corpus (4)

• On absolute nonshadowability of transitive maps
• Nonsmooth mappings with Lipschitz shadowing
• Generalizations of analogs of theorems of Maizel and Pliss and their application in Shadowing Theory
• Hölder stability for $C^r$ central translations