Shadowing in Linear Skew Products

Research output


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 the Hammel–Yorke–Grebogi conjecture concerning the interval of shadowability for a typical pseudotrajectory is not correct. The main technique is the reduction of the shadowing problem to the ruin problem for a simple random walk.

Original languageEnglish
Pages (from-to)979-987
Number of pages9
JournalJournal of Mathematical Sciences (United States)
Issue number6
Early online date19 Aug 2015
Publication statusPublished - 2015

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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