Shadowing in linear skew product
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Submission date: 30. Oct. 2014
published in: Zapiski naucnych seminarov POMI, 432 (2015), p. 261-273
with the following different title: Shadowing in linear skew products
MSC-Numbers: 37C50, 37D30, 60F10
Keywords and phrases: Holder shadowing, skew product
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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.