Article

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

Differential Equationsjournal2017en

ABI

Abstract

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.

Topics

Geometric Analysis and Curvature Flows Point processes and geometric inequalities Geometry and complex manifolds

Identifiers

DOI: 10.1134/s001226611703003x

Citations and references

Cited by 6 8 references

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