On Problems of Stability Theory for Weakly Hyperbolic Invariant Sets

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Abstract

Abstract: This paper presents a brief survey for the theory of stability of weakly hyperbolic invariant sets. It has been proved in several papers that I published along with Pliss and Sell that a weakly hyperbolic invariant set is stable even if the Lipschitz condition fails to hold. However, the uniqueness of leaves of a weakly hyperbolic invariant set of a perturbed system remains an open question. We show that this problem is connected to the so-called plaque expansivity conjecture in the theory of dynamical systems.

Original languageEnglish
Pages (from-to)191-196
Number of pages6
JournalVestnik St. Petersburg University: Mathematics
Volume53
Issue number2
DOIs
StatePublished - 1 Apr 2020

Scopus subject areas

  • Mathematics(all)

Keywords

  • leaf set
  • perturbed system
  • plaque expansivity
  • stability
  • uniqueness
  • weak hyperbolicity

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