Journal of Dynamics and Differential Equations

, Volume 28, Issue 1, pp 225–237

Oriented Shadowing Property and \(\Omega \)-Stability for Vector Fields

Article

DOI: 10.1007/s10884-014-9399-5

Cite this article as:
Gan, S., Li, M. & Tikhomirov, S.B. J Dyn Diff Equat (2016) 28: 225. doi:10.1007/s10884-014-9399-5

Abstract

We call that a vector field has the oriented shadowing property if for any \(\varepsilon >0\) there is \(d>0\) such that each \(d\)-pseudo orbit is \(\varepsilon \)-oriented shadowed by some real orbit. In this paper, we show that the \(C^1\)-interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the \(\Omega \)-stability.

Keywords

Vector fields Oriented shadowing \(\Omega \)-stability 

Mathematics Subject Classification

37C50 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.LMAM and School of Mathematical SciencesPeking UniversityBeijingPeople’s republic of China
  2. 2.School of Mathematical Sciences and LPMCNankai UniversityTianjinPeople’s Republic of China
  3. 3.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  4. 4.Chebyshev LaboratorySaint-Petersburg State UniversitySaint-PetersburgRussia

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