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On the stability of invariant sets of leaves of three-dimensional periodic systems. / Begun, N. A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 47, No. 3, 01.01.2014, p. 95-101.

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Harvard

Begun, NA 2014, 'On the stability of invariant sets of leaves of three-dimensional periodic systems', Vestnik St. Petersburg University: Mathematics, vol. 47, no. 3, pp. 95-101. https://doi.org/10.3103/S1063454114030030

APA

Begun, N. A. (2014). On the stability of invariant sets of leaves of three-dimensional periodic systems. Vestnik St. Petersburg University: Mathematics, 47(3), 95-101. https://doi.org/10.3103/S1063454114030030

Vancouver

Begun NA. On the stability of invariant sets of leaves of three-dimensional periodic systems. Vestnik St. Petersburg University: Mathematics. 2014 Jan 1;47(3):95-101. https://doi.org/10.3103/S1063454114030030

Author

Begun, N. A. / On the stability of invariant sets of leaves of three-dimensional periodic systems. In: Vestnik St. Petersburg University: Mathematics. 2014 ; Vol. 47, No. 3. pp. 95-101.

BibTeX

@article{d7b67c064ed14b8fb52abfe92887a9c5,
title = "On the stability of invariant sets of leaves of three-dimensional periodic systems",
abstract = "The small C1 perturbations of differential equations are studied. The concepts of a weakly hyperbolic set K and a leaf ϒ are introduced for a system of ordinary differential equations. The Lipschitz condition is not supposed. It is shown that, if the perturbation is small enough, then there exists a continuous mapping h : ϒ → ϒY, where ϒY is a leaf of the perturbed system.",
keywords = "Hyperbolic structures, Invariant set, Small perturbations, Stability",
author = "Begun, {N. A.}",
note = "Funding Information: ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research (project no. 13 01 00624). Publisher Copyright: {\textcopyright} Allerton Press, Inc., 2014. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",
year = "2014",
month = jan,
day = "1",
doi = "10.3103/S1063454114030030",
language = "English",
volume = "47",
pages = "95--101",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - On the stability of invariant sets of leaves of three-dimensional periodic systems

AU - Begun, N. A.

N1 - Funding Information: ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research (project no. 13 01 00624). Publisher Copyright: © Allerton Press, Inc., 2014. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The small C1 perturbations of differential equations are studied. The concepts of a weakly hyperbolic set K and a leaf ϒ are introduced for a system of ordinary differential equations. The Lipschitz condition is not supposed. It is shown that, if the perturbation is small enough, then there exists a continuous mapping h : ϒ → ϒY, where ϒY is a leaf of the perturbed system.

AB - The small C1 perturbations of differential equations are studied. The concepts of a weakly hyperbolic set K and a leaf ϒ are introduced for a system of ordinary differential equations. The Lipschitz condition is not supposed. It is shown that, if the perturbation is small enough, then there exists a continuous mapping h : ϒ → ϒY, where ϒY is a leaf of the perturbed system.

KW - Hyperbolic structures

KW - Invariant set

KW - Small perturbations

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84923361299&partnerID=8YFLogxK

U2 - 10.3103/S1063454114030030

DO - 10.3103/S1063454114030030

M3 - Article

AN - SCOPUS:84923361299

VL - 47

SP - 95

EP - 101

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 71239868