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Title: Coadjoint orbits of three-step free nilpotent Lie groups and time-optimal control problem
Authors: A.V.Podobryaev
Journal title: Doklady Mathematics
Year: 2020
Issue: 1
Volume: 102
Pages: 293--295
Citation:

A. V. Podobryaev, “Coadjoint orbits of three-step free nilpotent Lie groups and time-optimal control problem”, Doklady Mathematics, 102:1 (2020), 293–295

Abstract:

We describe coadjoint orbits for three-step free nilpotent Lie groups. It turns out that two-dimensional orbits have the same structure as coadjoint orbits of the Heisenberg group and the Engel group. We consider a time-optimal problem on three-step free nilpotent Lie groups with a set of admissible velocities in the first level of the Lie algebra. The behavior of normal extremal trajectories with initial covectors lying in two-dimensional coadjoint orbits is studied. Under some broad conditions on the set of admissible velocities (in particular, in the sub-Riemannian case) the corresponding extremal controls are periodic, constant, or asymptotically constant.