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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.