On the geometry of the reachability set of vector fields
Abdigappar NarmanovThe National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, 700174, UzbekistanS. S. SaitovaThe National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, 700174, Uzbekistan
Ochiq kirish: yoʻq
ABI
Annotatsiya
We study the geometry of the reachability set of a family of vector fields on a C ∞ manifold. We show that, for each real number T, the T-reachability set is a smooth submanifold of an orbit of codimension zero or one and that, on an arbitrary connected C ∞ manifold of dimension greater than one, there exists a system of three vector fields such that each 0-reachability set coincides with the manifold itself.
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