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MiS Preprint
48/2014

Oriented shadowing property and $\Omega$-stability for vector fields

Shaobo Gan, Ming Li and Sergey Tikhomirov

Abstract

We call that a vector field has the oriented shadowing property if for any $\epsilon > 0$ there is $d>0$ such that each $d$-pseudo orbit is $\epsilon$-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.

Received:
14.04.2014
Published:
22.04.2014
MSC Codes:
37C50
Keywords:
oriented shadowing, $\Omega$-stability, star vector fields

Related publications

inJournal
2016 Repository Open Access
Shaobo Gan, Ming Li and Sergey Tikhomirov

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

In: Journal of dynamics and differential equations, 28 (2016) 1, pp. 225-237