Oriented shadowing property and $Ω$-stability for vector fields

Shaobo Gan, Ming Li, Sergey B. Tikhomirov

Published 2014-04-14, updated 2014-08-11Version 2

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.