Vector Fields with the Oriented Shadowing Property

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.