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On the stability of invariant sets of leaves of three-dimensional periodic systems. / Begun, N. A.
в: Vestnik St. Petersburg University: Mathematics, Том 47, № 3, 01.01.2014, стр. 95-101.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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