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MiS Preprint
107/2014

Shadowing in linear skew product

Sergey Tikhomirov

Abstract

We consider linear skew product with the full shift in the base and non-zero Lyapunov exponent in the fiber. We provide sharp estimate for the precision of shadowing for a typical pseudotrajectory of finite length. This result suggests that the high-dimensional analogue of Hammel-Yorke-Grebogi's conjecture concerning the interval of shadowability for a typical pseudotrajectory is not correct. The main technique is reduction of shadowing problem to the ruin problem for one-dimensional random walk.

Received:
Oct 30, 2014
Published:
Nov 7, 2014
MSC Codes:
37C50, 37D30, 60F10
Keywords:
Holder shadowing, skew product

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