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

Bizyaev I. A.; Borisov A. V.; Kilin A. A.; Mamaev I. S.

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

2017, Vol. 13, No. 1, pp. 129-146

Author(s): Bizyaev I. A., Borisov A. V., Kilin A. A., Mamaev I. S.

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

Citation: Bizyaev I. A., Borisov A. V., Kilin A. A., Mamaev I. S., Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 1, pp. 129-146

DOI:10.20537/nd1701009

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