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

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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.

Original languageEnglish
JournalVestnik St. Petersburg University: Mathematics
Volume48
Issue number1
DOIs
StatePublished - 3 Mar 2015

Scopus subject areas

  • Mathematics(all)

Keywords

  • hyperbolic structures
  • invariant set
  • small perturbations
  • stability
  • structural stability
  • weakly hyperbolic set

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