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Sibirsk. Mat. Zh., 2016, Volume 57, Number 1, Pages 3–9 (Mi smj2724)  

On the sub-Riemannian geodesic flow for the Goursat distribution

S. V. Agapovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: Under consideration is the sub-Riemannian geodesic flow for the Goursat distribution. We find the level surfaces of the first integrals that are in involution and study the trajectories in the phase space whose projections to the horizontal plane are closed curves.

Keywords: optimal control, sub-Riemannian geometry, Goursat distribution, geodesic flow.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.В25.31.0029
Russian Foundation for Basic Research 12-01-00124-а
The author was supported by the Government of the Russian Federation (Grant 14.B25.31.0029) and the Russian Foundation for Basic Research (Grant 12-01-00124-a).


DOI: https://doi.org/10.17377/smzh.2016.57.101

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English version:
Siberian Mathematical Journal, 2016, 57:1, 1–6

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 30.12.2014

Citation: S. V. Agapov, “On the sub-Riemannian geodesic flow for the Goursat distribution”, Sibirsk. Mat. Zh., 57:1 (2016), 3–9; Siberian Math. J., 57:1 (2016), 1–6

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