Oriented shadowing property and Ω-stability for vector fields

Shaobo Gan, Ming Li, and Sergey Tikhomirov

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Submission date: 14. Apr. 2014
Pages: 12
published in: Journal of dynamics and differential equations, 28 (2016) 1, p. 225-237 
DOI number (of the published article): 10.1007/s10884-014-9399-5
Bibtex
MSC-Numbers: 37C50
Keywords and phrases: oriented shadowing, $\Omega$-stability, star vector fields
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Abstract:
We call that a vector field has the oriented shadowing property if for any 𝜖 > 0 there is d > 0 such that each d-pseudo orbit is 𝜖-oriented shadowed by some real orbit. In this paper, we show that the C¹-interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the Ω-stability.