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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.  Full text:
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English version: Journal of Mathematical Sciences (New York), 2015, 209:6,  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, 
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