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Regular and Chaotic Dynamics, 2016, Volume 21, Issue 6, Pages 759–774
DOI: https://doi.org/10.1134/S1560354716060125 (Mi rcd222) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Integrability and Nonintegrability of Sub-Riemannian Geodesic Flows on Carnot Groups

Ivan A. Bizyaeva, Alexey V. Borisovba, Alexander A. Kilina, Ivan S. Mamaevc

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409 Russia
c Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
Citations (15)
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DOI: https://doi.org/10.1134/S1560354716060125
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
Dynasty Foundation
Russian Foundation for Basic Research 14-01-00395-a
Russian Science Foundation 14-19-01303
The work of I. A. Bizyaev and A. A. Kilin was carried out within the framework of the state assignment for institutions of higher education. The work of I. A. Bizyaev was also partially supported by the Dynasty Foundation. The work of A. V. Borisov was supported by the RFBR grant No. 14-01-00395-a. The work of I. S. Mamaev (Section 3) was supported by the Russian Science Foundation (project No. 14-19-01303).
Received: 16.10.2016
Accepted: 20.11.2016
Bibliographic databases:
Document Type: Article
MSC: 53C17, 37C10
Language: English
Citation: Ivan A. Bizyaev, Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Integrability and Nonintegrability of Sub-Riemannian Geodesic Flows on Carnot Groups”, Regul. Chaotic Dyn., 21:6 (2016), 759–774
Citation in format AMSBIB
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\by Ivan A. Bizyaev, Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper Integrability and Nonintegrability of Sub-Riemannian Geodesic Flows on Carnot Groups
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 6
\pages 759--774
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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