On the stability of invariant sets of leaves of three-dimensional periodic systems

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4 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)95-101
Number of pages7
JournalVestnik St. Petersburg University: Mathematics
Volume47
Issue number3
DOIs
StatePublished - 1 Jan 2014

Scopus subject areas

  • Mathematics(all)

Keywords

  • Hyperbolic structures
  • Invariant set
  • Small perturbations
  • Stability

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