Email this article Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups
- Authors: Bizyaev I.A.1, Borisov A.V.1,2, Kilin A.A.1, Mamaev I.S.3
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Affiliations:
- Udmurt State University
- National Research Nuclear University “MEPhI”
- Izhevsk State Technical University
- Issue: Vol 21, No 6 (2016)
- Pages: 759-774
- Section: On the 70th Birthday of Nikolai N. Nekhoroshev Special Memorial Issue. Part 1
- URL: https://ogarev-online.ru/1560-3547/article/view/218444
- DOI: https://doi.org/10.1134/S1560354716060125
- ID: 218444
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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.
About the authors
Ivan A. Bizyaev
Udmurt State University
Author for correspondence.
Email: bizaev_90@mail.ru
Russian Federation, ul. Universitetskaya 1, Izhevsk, 426034
Alexey V. Borisov
Udmurt State University; National Research Nuclear University “MEPhI”
Email: bizaev_90@mail.ru
Russian Federation, ul. Universitetskaya 1, Izhevsk, 426034; Kashirskoe sh. 31, Moscow, 115409
Alexander A. Kilin
Udmurt State University
Email: bizaev_90@mail.ru
Russian Federation, ul. Universitetskaya 1, Izhevsk, 426034
Ivan S. Mamaev
Izhevsk State Technical University
Email: bizaev_90@mail.ru
Russian Federation, ul. Studencheskaya 7, Izhevsk, 426069
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