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MiS Preprint

Shadowing in linear skew product

Sergey Tikhomirov


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.

MSC Codes:
37C50, 37D30, 60F10
Holder shadowing, skew product

Related publications

2015 Journal Open Access
Sergey Tikhomirov

Shadowing in linear skew products

In: Zapiski naucnych seminarov POMI, 432 (2015), pp. 261-273
2015 Repository Open Access
Sergey Tikhomirov

Shadowing in linear skew products

In: Journal of mathematical sciences, 209 (2015) 6, pp. 979-987