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Zap. Nauchn. Sem. POMI, 2015, Volume 432, Pages 261–273 (Mi znsl6120)  

Shadowing in linear skew products

S. Tikhomirovab

a Chebyshev Laboratory, St. Petersburg State Univeristy, 14th line of Vasilievsky Island, 29B, St. Petersburg 199178, Russia
b Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany

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.

Key words and phrases: shadowing, skew product, random walk, large deviation principle.

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English version:
Journal of Mathematical Sciences (New York), 2015, 209:6, 979–987

Document Type: Article
UDC: 517.9
Received: 03.11.2014
Language: English

Citation: S. Tikhomirov, “Shadowing in linear skew products”, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Zap. Nauchn. Sem. POMI, 432, POMI, St. Petersburg, 2015, 261–273; J. Math. Sci. (N. Y.), 209:6 (2015), 979–987

Citation in format AMSBIB
\Bibitem{Tik15}
\by S.~Tikhomirov
\paper Shadowing in linear skew products
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 432
\pages 261--273
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6120}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 6
\pages 979--987
\crossref{https://doi.org/10.1007/s10958-015-2541-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84939459016}


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