English

Shadowing in linear skew products

Dynamical Systems 2014-11-07 v1 Probability

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.

Keywords

Cite

@article{arxiv.1411.1541,
  title  = {Shadowing in linear skew products},
  author = {Sergey Tikhomirov},
  journal= {arXiv preprint arXiv:1411.1541},
  year   = {2014}
}

Comments

14 pages

R2 v1 2026-06-22T06:49:43.800Z