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MiS Preprint
106/2013
Hölder Shadowing on Finite Intervals
Sergey Tikhomirov
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, Yorke and Grebogi 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.
