Geometry of orbits of vector fields and singular foliations

A. Ya. Narmanov

Contemporary Mathematics. Fundamental Directions, Contemporary problems in mathematics and physics, Tome 65 (2019) no. 1, pp. 54-71.

Résumé

The subject of this paper is the geometry of orbits of a family of smooth vector fields defined on a smooth manifold and singular foliations generated by the orbits. As is well known, the geometry of orbits of vector fields is one of the main subjects of investigation in geometry and control theory. Here we propose some author's results on this problem. Throughout this paper, the smoothness means $C^{\infty}$-smoothness.

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