Oriented Shadowing Property and \(\Omega \)-Stability for Vector Fields
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- Gan, S., Li, M. & Tikhomirov, S.B. J Dyn Diff Equat (2016) 28: 225. doi:10.1007/s10884-014-9399-5
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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.