Perturbations of weakly hyperbolic invariant sets of two-dimension periodic systems

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Perturbations of weakly hyperbolic invariant sets of two-dimension periodic systems. / Begun, N. A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 48, No. 1, 03.03.2015.

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

BibTeX

@article{a611cf0a661d4a4db27a673c549e3673,

title = "Perturbations of weakly hyperbolic invariant sets of two-dimension periodic systems",

abstract = "The question of structural stability is one of the most important areas in a present-day theory of differential equations. In this paper, we study small C1 perturbations of a systems of differential equations. We introduce the concepts of a weakly hyperbolic invariant set K and leaf Y for a system of ordinary differential equations. The Lipschitz condition is not assumed. We show that, if the perturbation is small enough, then there is a continuous mapping h, i.e., K → KY, where KY is a weakly hyperbolic set of the perturbed equation system. Moreover, we show that h(Y) is a leaf of the perturbed system.",

keywords = "hyperbolic structures, invariant set, small perturbations, stability, structural stability, weakly hyperbolic set",

author = "Begun, {N. A.}",

year = "2015",

month = mar,

day = "3",

doi = "10.3103/S1063454115010033",

language = "English",

volume = "48",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Perturbations of weakly hyperbolic invariant sets of two-dimension periodic systems

AU - Begun, N. A.

PY - 2015/3/3

Y1 - 2015/3/3

N2 - The question of structural stability is one of the most important areas in a present-day theory of differential equations. In this paper, we study small C1 perturbations of a systems of differential equations. We introduce the concepts of a weakly hyperbolic invariant set K and leaf Y for a system of ordinary differential equations. The Lipschitz condition is not assumed. We show that, if the perturbation is small enough, then there is a continuous mapping h, i.e., K → KY, where KY is a weakly hyperbolic set of the perturbed equation system. Moreover, we show that h(Y) is a leaf of the perturbed system.

AB - The question of structural stability is one of the most important areas in a present-day theory of differential equations. In this paper, we study small C1 perturbations of a systems of differential equations. We introduce the concepts of a weakly hyperbolic invariant set K and leaf Y for a system of ordinary differential equations. The Lipschitz condition is not assumed. We show that, if the perturbation is small enough, then there is a continuous mapping h, i.e., K → KY, where KY is a weakly hyperbolic set of the perturbed equation system. Moreover, we show that h(Y) is a leaf of the perturbed system.

KW - hyperbolic structures

KW - invariant set

KW - small perturbations

KW - stability

KW - structural stability

KW - weakly hyperbolic set

UR - http://www.scopus.com/inward/record.url?scp=84925336783&partnerID=8YFLogxK

U2 - 10.3103/S1063454115010033

DO - 10.3103/S1063454115010033

M3 - Article

AN - SCOPUS:84925336783

VL - 48

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 71239807