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

  • On the 70th Birthday of Nikolai N. Nekhoroshev Special Memorial Issue. Part 1
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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.

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Authors and Affiliations

  1. Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia

    Ivan A. Bizyaev, Alexey V. Borisov & Alexander A. Kilin

  2. National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409, Russia

    Alexey V. Borisov

  3. Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069, Russia

    Ivan S. Mamaev

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  1. Ivan A. Bizyaev
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Bizyaev, I.A., Borisov, A.V., Kilin, A.A. et al. Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups. Regul. Chaot. Dyn. 21, 759–774 (2016). https://doi.org/10.1134/S1560354716060125

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