Oriented shadowing property and \(\Omega\)-stability for vector fields

Oriented shadowing property and \(\Omega\)-stability for vector fields

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 oriente...

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Veröffentlicht in:arXiv.org 2014-08
Hauptverfasser: Gan, Shaobo, Li, Ming, Tikhomirov, Sergey B
Format: Artikel
Sprache:eng
Schlagworte:
Fields (mathematics)
Stability
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Zusammenfassung: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.
ISSN:2331-8422