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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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:
14.04.14
Published:
22.04.14
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