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MiS Preprint

Hölder Shadowing on Finite Intervals

Sergey Tikhomirov


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.

Nov 19, 2013
Nov 21, 2013
MSC Codes:
37C50, 37D20
Hoelder shadowing, structural stability, exponential dichotomy, sublinear growth

Related publications

2015 Repository Open Access
Sergey Tikhomirov

Hölder shadowing on finite intervals

In: Ergodic theory and dynamical systems, 35 (2015) 6, pp. 2000-2016