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Hölder shadowing on finite intervals. / Tikhomirov, Sergey.

в: Ergodic Theory and Dynamical Systems, Том 35, № 6, 2014, стр. 2000-2016.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

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Tikhomirov, S 2014, 'Hölder shadowing on finite intervals', Ergodic Theory and Dynamical Systems, Том. 35, № 6, стр. 2000-2016. https://doi.org/10.1017/etds.2014.7, https://doi.org/10.1017/etds.2014.7

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Tikhomirov, Sergey. / Hölder shadowing on finite intervals. в: Ergodic Theory and Dynamical Systems. 2014 ; Том 35, № 6. стр. 2000-2016.

BibTeX

@article{6ced0920aacd492bb939911953f3b71e,
title = "H{\"o}lder shadowing on finite intervals",
abstract = "For any $\theta, \omega>1/2$, we prove that, if any $d$-pseudotrajectory of length $∼1/d\omega$ of a diffeomorphism $f\in C^2$ can be $d\theta$-shadowed by an exact trajectory, then f is structurally stable. Previously it was conjectured [S. M. Hammel et al. Do numerical orbits of chaotic dynamical processes represent true orbits. J. Complexity3 (1987), 136–145; S. M. Hammel et al. Numerical orbits of chaotic processes represent true orbits. Bull. Amer. Math. Soc.19 (1988), 465–469] that for $\theta=\omega=1/2$, this property holds for a wide class of non-uniformly hyperbolic diffeomorphisms. In the proof, we introduce the notion of a sublinear growth property for inhomogeneous linear equations and prove that it implies exponential dichotomy.",
keywords = "Holder shadowing, exponential dichotomy, sublinear growth property",
author = "Sergey Tikhomirov",
year = "2014",
doi = "10.1017/etds.2014.7",
language = "English",
volume = "35",
pages = "2000--2016",
journal = "Ergodic Theory and Dynamical Systems",
issn = "0143-3857",
publisher = "Cambridge University Press",
number = "6",

}

RIS

TY - JOUR

T1 - Hölder shadowing on finite intervals

AU - Tikhomirov, Sergey

PY - 2014

Y1 - 2014

N2 - For any $\theta, \omega>1/2$, we prove that, if any $d$-pseudotrajectory of length $∼1/d\omega$ of a diffeomorphism $f\in C^2$ can be $d\theta$-shadowed by an exact trajectory, then f is structurally stable. Previously it was conjectured [S. M. Hammel et al. Do numerical orbits of chaotic dynamical processes represent true orbits. J. Complexity3 (1987), 136–145; S. M. Hammel et al. Numerical orbits of chaotic processes represent true orbits. Bull. Amer. Math. Soc.19 (1988), 465–469] that for $\theta=\omega=1/2$, this property holds for a wide class of non-uniformly hyperbolic diffeomorphisms. In the proof, we introduce the notion of a sublinear growth property for inhomogeneous linear equations and prove that it implies exponential dichotomy.

AB - For any $\theta, \omega>1/2$, we prove that, if any $d$-pseudotrajectory of length $∼1/d\omega$ of a diffeomorphism $f\in C^2$ can be $d\theta$-shadowed by an exact trajectory, then f is structurally stable. Previously it was conjectured [S. M. Hammel et al. Do numerical orbits of chaotic dynamical processes represent true orbits. J. Complexity3 (1987), 136–145; S. M. Hammel et al. Numerical orbits of chaotic processes represent true orbits. Bull. Amer. Math. Soc.19 (1988), 465–469] that for $\theta=\omega=1/2$, this property holds for a wide class of non-uniformly hyperbolic diffeomorphisms. In the proof, we introduce the notion of a sublinear growth property for inhomogeneous linear equations and prove that it implies exponential dichotomy.

KW - Holder shadowing

KW - exponential dichotomy

KW - sublinear growth property

U2 - 10.1017/etds.2014.7

DO - 10.1017/etds.2014.7

M3 - Article

VL - 35

SP - 2000

EP - 2016

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 6

ER -

ID: 5799401