Elena Sachkova

    Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
    Ailamazyan Program Systems Institute of RAS


    Sachkov Y. L., Sachkova E. F.
    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.
    Keywords: sub-Riemannian geometry, abnormal trajectories, geometric control
    Citation: Sachkov Y. L., Sachkova E. F.,  Abnormal Extremals in the Sub-Riemannian Problem with Growth Vector $(2, 3, 5, 8, 14)$, Rus. J. Nonlin. Dyn., 2023, Vol. 19, no. 4, pp.  559-573
    Sachkov Y. L., Sachkova E. F.
    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.
    Keywords: sub-Riemannian geometry, abnormal extremals, symmetries
    Citation: 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), Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp.  577-585

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