Vector Fields with the Oriented Shadowing Property

Details Vector Fields with the Oriented Shadowing Property Vector Fields with the Oriented Shadowing Property

2010-10-16

arxiv.org/abs/1010.3308v1

Journal of Differential Equations, Volume 248, Issue 6, 15 March 2010, Pages 1345-1375

Mathematics

Dynamical Systems

42 pages

Scientific paper

10.1016/j.jde.2009.09.024

We give a description of the $\Cone$-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 $\Bb$ of vector fields that are not structurally stable is introduced. It is shown that the set $\Int^1(\OrientSh\setminus\Bb)$ coincides with the set of structurally stable vector fields. An example of a field of the class $\Bb$ belonging to $\Int^1(\OrientSh)$ is given. Bibliography: 18 titles.

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