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Russian Journal of Nonlinear Dynamics, 2023, Volume 19, Number 4, Pages 559–573
DOI: https://doi.org/10.20537/nd231104 (Mi nd868) 		 
Mathematical problems of nonlinearity

Abnormal Extremals in the Sub-Riemannian Problem with Growth Vector $(2, 3, 5, 8, 14)$

Yu. L. Sachkov, E. F. Sachkova

Program Systems Institute Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
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DOI: https://doi.org/10.20537/nd231104
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.
Keywords: sub-Riemannian geometry, abnormal trajectories, geometric control
Funding agency Grant number
Russian Science Foundation 22-21-00877
Subsections 4.1–4.3 of the paper were written by E. Sachkova, and the rest sections were written by Yu. Sachkov. The work of E. Sachkova is supported by the Russian Science Foundation under grant 22-21-00877 (https://rscf.ru/en/project/22-21-00877/) and performed at the Ailamazyan Program Systems Institute of the Russian Academy of Sciences.
Received: 30.07.2023
Accepted: 28.10.2023
Document Type: Article
MSC: 53C17
Language: English
Citation: Yu. L. Sachkov, E. F. Sachkova, “Abnormal Extremals in the Sub-Riemannian Problem with Growth Vector $(2, 3, 5, 8, 14)$”, Rus. J. Nonlin. Dyn., 19:4 (2023), 559–573
Citation in format AMSBIB
\Bibitem{SacSac23}
\by Yu. L. Sachkov, E. F. Sachkova
\paper Abnormal Extremals in the Sub-Riemannian Problem with Growth Vector $(2, 3, 5, 8, 14)$
\jour Rus. J. Nonlin. Dyn.
\yr 2023
\vol 19
\issue 4
\pages 559--573
\mathnet{http://mi.mathnet.ru/nd868}
\crossref{https://doi.org/10.20537/nd231104}
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