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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 304, Pages 49–67
DOI: https://doi.org/10.4213/tm3961 (Mi tm3961) 		 
This article is cited in 9 scientific papers (total in 9 papers)

A Sub-Finsler Problem on the Cartan Group

A. A. Ardentova, E. Le Donneb, Yu. L. Sachkova

a Ailamazyan Program Systems Institute of Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
b Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 Jyväskylä, Finland
Full-text PDF (1139 kB) Citations (9)
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DOI: https://doi.org/10.4213/tm3961
Abstract: We study a sub-Finsler geometric problem on the free nilpotent group of rank $2$ and step $3$. Such a group is also called the Cartan group and has a natural structure of Carnot group, which we metrize by considering the $\ell _\infty $ norm on its first layer. We adopt the point of view of time-optimal control theory. We characterize extremal curves via the Pontryagin maximum principle. We describe abnormal and singular arcs and construct the bang–bang flow.
Funding agency Grant number
Russian Science Foundation 17-11-01387
Academy of Finland 288501
European Research Council 713998
Sections 1–3 of the paper are written by E. Le Donne, and Sections 4–7 are written by A. Ardentov and Yu. Sachkov. The work of A. Ardentov and Yu. Sachkov is supported by the Russian Science Foundation under grant 17-11-01387 and performed in the Ailamazyan Program Systems Institute of Russian Academy of Sciences. E. Le Donne was partially supported by the Academy of Finland (grant 288501 “Geometry of subRiemannian groups”) and by the European Research Council (ERC Starting Grant 713998 GeoMeG “Geometry of metric groups”).
Received: August 30, 2018
Revised: October 8, 2018
Accepted: December 6, 2018
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 304, Pages 42–59
DOI: https://doi.org/10.1134/S0081543819010048
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
MSC: 53C17, 43A80, 22E25, 22F30, 14M17, 49J15
Language: Russian
Citation: A. A. Ardentov, E. Le Donne, Yu. L. Sachkov, “A Sub-Finsler Problem on the Cartan Group”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 49–67; Proc. Steklov Inst. Math., 304 (2019), 42–59
Citation in format AMSBIB
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\paper A Sub-Finsler Problem on the Cartan Group
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 49--67
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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    • This publication is cited in the following 9 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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