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Nelin. Dinam., 2019, Volume 15, Number 4, Pages 577–585 (Mi nd685)  

Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)

Yu. L. Sachkov, E. F. Sachkova

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

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.

Keywords: sub-Riemannian geometry, abnormal extremals, symmetries

Funding Agency Grant Number
Russian Science Foundation 17-11-01387
The work of Yu. L. Sachkov and E. F. Sachkova was supported by the Russian Science Foundation under grant 17-11-01387 and performed at the Ailamazyan Program Systems Institute of the Russian Academy of Sciences.


DOI: https://doi.org/10.20537/nd190417

Full text: PDF file (248 kB)
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MSC: 93C15
Received: 30.05.2019
Accepted:01.10.2019

Citation: Yu. L. Sachkov, E. F. Sachkova, “Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)”, Nelin. Dinam., 15:4 (2019), 577–585

Citation in format AMSBIB
\Bibitem{SacSac19}
\by Yu. L. Sachkov, E. F. Sachkova
\paper Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 4
\pages 577--585
\mathnet{http://mi.mathnet.ru/nd685}
\crossref{https://doi.org/10.20537/nd190417}


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