Elena Sachkova
Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
Ailamazyan Program Systems Institute of RAS
Publications:
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Sachkov Y. L., Sachkova E. F.
Abnormal Extremals in the Sub-Riemannian Problem with Growth Vector $(2, 3, 5, 8, 14)$
2023, Vol. 19, no. 4, pp. 559-573
Abstract
We study the left-invariant sub-Riemannian problem on the free nilpotent Lie group of
rank 2 and step 5. We describe some abnormal trajectories and some properties of the set filled
by nice abnormal trajectories starting at the identity of the group.
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Sachkov Y. L., Sachkova E. F.
Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)
2019, Vol. 15, no. 4, pp. 577-585
Abstract
The left-invariant sub-Riemannian problem with the growth vector (2, 3, 5, 8) is considered.
A two-parameter group of infinitesimal symmetries consisting of rotations and dilations
is described. The abnormal geodesic flow is factorized modulo the group of symmetries. A parameterization
of the vertical part of abnormal geodesic flow is obtained.
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