Preprint 107/2014

Shadowing in linear skew product

Sergey Tikhomirov

Contact the author: Please use for correspondence this email.
Submission date: 30. Oct. 2014
Pages: 16
published as: Shadowing in linear skew products.
In: Journal of mathematical sciences, 209 (2015) 6, p. 979-987 
DOI number (of the published article): 10.1007/s10958-015-2541-z
published as: Shadowing in linear skew products.
In: Zapiski naucnych seminarov POMI, 432 (2015), p. 261-273 
MSC-Numbers: 37C50, 37D30, 60F10
Keywords and phrases: Holder shadowing, skew product
Download full preprint: PDF (144 kB)

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.

26.03.2023, 03:09