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Geometry of Orbits of Vector Fields and Singular Foliations

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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 several author’s results on this problem. Throughout this paper, smoothness means C∞-smoothness.

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Authors and Affiliations

  1. National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan

    A. Ya. Narmanov

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  1. A. Ya. Narmanov
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Correspondence to A. Ya. Narmanov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 65, No. 1, Contemporary Problems in Mathematics and Physics, 2019.

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Narmanov, A.Y. Geometry of Orbits of Vector Fields and Singular Foliations. J Math Sci 265, 52–68 (2022). https://doi.org/10.1007/s10958-022-06044-y

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