On the Stability of Sheet Invariant Sets of Two-Dimensional Periodic Systems

被引：5

作者：

Begun, N. A. ^{[1
]}

机构：

[1] St Petersburg State Univ, Univ Skaya Nab 7-9, St Petersburg 199034, Russia

来源：

VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS | 2012年 / 45卷 / 04期

关键词：

stability; invariant set; small perturbations; hyperbolic structures;

D O I：

10.3103/S1063454112040024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper small C-1-perturbations of differential equations are considered. The concepts of a weakly hyperbolic set K and a sheet gamma 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: gamma -> gamma(Y), where gamma(Y) is a sheet of the perturbed system.

引用

页码：145 / 152

页数：8