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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 432, Pages 261–273
(Mi znsl6120)
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This article is cited in 2 scientific papers (total in 2 papers)
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.
Received: 03.11.2014
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
Linking options:
https://www.mathnet.ru/eng/znsl6120 https://www.mathnet.ru/eng/znsl/v432/p261
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Abstract page: | 234 | Full-text PDF : | 60 | References: | 47 |
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