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Shadowing in Linear Skew Products. / Tikhomirov, S.

In: Journal of Mathematical Sciences (United States), Vol. 209, No. 6, 2015, p. 979-987.

Research output: Contribution to journal › Article › peer-review

Harvard

Tikhomirov, S 2015, 'Shadowing in Linear Skew Products', Journal of Mathematical Sciences (United States), vol. 209, no. 6, pp. 979-987. https://doi.org/10.1007/s10958-015-2541-z

APA

Tikhomirov, S. (2015). Shadowing in Linear Skew Products. Journal of Mathematical Sciences (United States), 209(6), 979-987. https://doi.org/10.1007/s10958-015-2541-z

Vancouver

Tikhomirov S. Shadowing in Linear Skew Products. Journal of Mathematical Sciences (United States). 2015;209(6):979-987. https://doi.org/10.1007/s10958-015-2541-z

Author

Tikhomirov, S. / Shadowing in Linear Skew Products. In: Journal of Mathematical Sciences (United States). 2015 ; Vol. 209, No. 6. pp. 979-987.

BibTeX

@article{dc6df98fb8ac4cd8bccde0ec96c09d61,
title = "Shadowing in Linear Skew Products",
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.",
keywords = "Manifold, Large Deviation Principle, Simple Random Walk, Positive Lyapunov Exponent, True Orbit",
author = "S. Tikhomirov",
note = "Tikhomirov, S. Shadowing in Linear Skew Products. J Math Sci 209, 979–987 (2015). https://doi.org/10.1007/s10958-015-2541-z",
year = "2015",
doi = "10.1007/s10958-015-2541-z",
language = "English",
volume = "209",
pages = "979--987",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

TY - JOUR

T1 - Shadowing in Linear Skew Products

AU - Tikhomirov, S.

N1 - Tikhomirov, S. Shadowing in Linear Skew Products. J Math Sci 209, 979–987 (2015). https://doi.org/10.1007/s10958-015-2541-z

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Manifold

KW - Large Deviation Principle

KW - Simple Random Walk

KW - Positive Lyapunov Exponent

KW - True Orbit

UR - http://www.scopus.com/inward/record.url?scp=84939459016&partnerID=8YFLogxK

U2 - 10.1007/s10958-015-2541-z

DO - 10.1007/s10958-015-2541-z

M3 - Article

AN - SCOPUS:84939459016

VL - 209

SP - 979

EP - 987

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 43393133