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

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4 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)145-152
Number of pages8
JournalVestnik St. Petersburg University: Mathematics
Volume45
Issue number4
DOIs
StatePublished - 20 Dec 2012

Scopus subject areas

  • Mathematics(all)

Keywords

  • hyperbolic structures
  • invariant set
  • small perturbations
  • stability

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