Open AccessGeometry of Orbits of Vector Fields and Singular Foliations
Author(s) -
A. Ya. Narmanov,
Нарманов Абдигаппар Якубович
Publication year - 2019
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2019-65-1-54-71
Subject(s) - smoothness , vector field , manifold (fluid mechanics) , geometry , mathematics , fundamental vector field , mathematical analysis , engineering , mechanical engineering , lie conformal algebra , lie group , adjoint representation of a lie algebra
The subject of this paper is the geometry of orbits of a family of smooth vector elds dened on a smooth manifold and singular foliations generated by the orbits. As is well known, the geometry of orbits of vector elds 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∞-smoothness.