TY - JOUR

T1 - On the stability of sheet invariant sets of two-dimensional periodic systems

AU - Begun, N. A.

N1 - Funding Information: This work was financially supported in part by the Ministry of Education and Science of the Russian Federation, Federal Targeted Program “Scientific and Pedagogical Personnel of Innovation Driven Rus sia,” project no. 2010 1.1 111 128 033. Copyright: Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2012/12/20

Y1 - 2012/12/20

N2 - In the paper small C1-perturbations of differential equations are considered. The concepts of a weakly hyperbolic set K and a sheet Υ{hooked} for a system of ordinary differential equation are introduced. Lipschitz property is not assumed to hold. It is shown that if the perturbation is small enough, then there is a continuous mapping h: Υ{hooked} → Υ{hooked}Y, where Υ{hooked}Y is a sheet of the perturbed system.

AB - In the paper small C1-perturbations of differential equations are considered. The concepts of a weakly hyperbolic set K and a sheet Υ{hooked} for a system of ordinary differential equation are introduced. Lipschitz property is not assumed to hold. It is shown that if the perturbation is small enough, then there is a continuous mapping h: Υ{hooked} → Υ{hooked}Y, where Υ{hooked}Y is a sheet of the perturbed system.

KW - hyperbolic structures

KW - invariant set

KW - small perturbations

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=84872193485&partnerID=8YFLogxK

U2 - 10.3103/S1063454112040024

DO - 10.3103/S1063454112040024

M3 - Article

AN - SCOPUS:84872193485

VL - 45

SP - 145

EP - 152

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -