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Russian Journal of Nonlinear Dynamics, 2019, Volume 15, Number 4, Pages 577–585
DOI: https://doi.org/10.20537/nd190417 (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
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DOI: https://doi.org/10.20537/nd190417
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.
Received: 30.05.2019
Accepted: 01.10.2019
Bibliographic databases:
Document Type: Article
MSC: 93C15
Language: English
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)”, Rus. J. Nonlin. Dyn., 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 Rus. J. Nonlin. Dyn.
\yr 2019
\vol 15
\issue 4
\pages 577--585
\mathnet{http://mi.mathnet.ru/nd685}
\crossref{https://doi.org/10.20537/nd190417}
\elib{https://elibrary.ru/item.asp?id=43292204}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85085143781}
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