Shadowing in linear skew products

Sergey Tikhomirov

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arXiv · 1411.1541

Shadowing in linear skew products

Sergey Tikhomirov

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Abstract

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

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Sergey Tikhomirov. 2014-11-06. Shadowing in linear skew products. https://arxiv.org/abs/1411.1541

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