Shadowing in Linear Skew Products

Research output

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 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)
Volume209
Issue number6
Early online date19 Aug 2015
DOIs
Publication statusPublished - 2015

Scopus subject areas

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

Fingerprint Dive into the research topics of 'Shadowing in Linear Skew Products'. Together they form a unique fingerprint.

  • Cite this