Vector fields with the oriented shadowing property

We give a description of the C 1 -interior ( Int 1 ( OrientSh ) ) of the set of smooth vector fields on a smooth closed manifold that have the oriented shadowing property. A special class B of vector fields that are not structurally stable is introduced. It is shown that the set Int 1 ( OrientSh ∖ B...

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Bibliographic Details
Published in:Journal of Differential Equations 2010-03, Vol.248 (6), p.1345-1375
Main Authors: Pilyugin, Sergei Yu, Tikhomirov, Sergey B.
Format: Article
Language:English
Subjects:
Oriented shadowing
Structural stability
Vector fields
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Summary:We give a description of the C 1 -interior ( Int 1 ( OrientSh ) ) of the set of smooth vector fields on a smooth closed manifold that have the oriented shadowing property. A special class B of vector fields that are not structurally stable is introduced. It is shown that the set Int 1 ( OrientSh ∖ B ) coincides with the set of structurally stable vector fields. An example of a field of the class B belonging to Int 1 ( OrientSh ) is given. Bibliography: 18 titles.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2009.09.024