On the Geometry of Vector Fields

It is well known that the study of the geometry and topology of the attainability set of a family of vector fields is one of the main tasks of the qualitative control theory, which is closely related to the geometry of orbits of vector fields. In this paper, we discuss the authors' results on the geometry of the attainability set of a family of vector fields: the results on the geometry of $T$-attainability sets and the geometry of orbits of Killing vector fields.