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This article is cited in 14 scientific papers (total in 14 papers)
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.
Received: 16.10.2016 Accepted: 20.11.2016
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
Linking options:
https://www.mathnet.ru/eng/nd555 https://www.mathnet.ru/eng/nd/v13/i1/p129
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