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Nelin. Dinam., 2017, Volume 13, Number 1, Pages 129–146 (Mi nd555)  

Translated papers

Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups

I. A. Bizyaeva, A. V. Borisovab, A. A. Kilina, I. S. Mamaevac

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
b National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409, Russia
c M.T.Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069, Russia

Abstract: This paper is concerned with two systems from sub-Riemannian geometry. One of them is defined by a Carnot group with three generatrices and growth vector (3, 6, 14), the other is defined by two generatrices and growth vector (2, 3, 5, 8). Using a Poincaré map, the nonintegrability of the above systems in the general case is shown. In addition, particular cases are presented in which there exist additional first integrals.

Keywords: sub-Riemannian geometry, Carnot group, Poincaré map, first integrals

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 15-08-09261-а
15-08-09093-а


DOI: https://doi.org/10.20537/nd1701009

Full text: PDF file (2888 kB)
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English version:
Regular and Chaotic Dynamics, 2016, 21:6, 759–774

Document Type: Article
UDC: 17.93
MSC: 53C17, 37C10
Received: 16.10.2016

Citation: I. A. Bizyaev, A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups”, Nelin. Dinam., 13:1 (2017), 129–146; Regular and Chaotic Dynamics, 21:6 (2016), 759–774

Citation in format AMSBIB
\Bibitem{BizBorKil17}
\by I.~A.~Bizyaev, A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 1
\pages 129--146
\mathnet{http://mi.mathnet.ru/nd555}
\crossref{https://doi.org/10.20537/nd1701009}
\elib{http://elibrary.ru/item.asp?id=28841005}
\transl
\jour Regular and Chaotic Dynamics
\yr 2016
\vol 21
\issue 6
\pages 759--774
\crossref{https://doi.org/10.1134/S1560354716060125}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85006247392}


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