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arXiv · 1010.3308

Vector Fields with the Oriented Shadowing Property

Sergei Yu. Pilyugin·Sergey Tikhomirov
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Abstract

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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Sergei Yu. Pilyugin, Sergey Tikhomirov. 2010-10-16. Vector Fields with the Oriented Shadowing Property. https://doi.org/10.1016/j.jde.2009.09.024

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