Geodesic
Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 1, pp. 129-146

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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, first integrals.
Mots-clés : Carnot group, Poincaré map 
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     author = {I. A. Bizyaev and A. V. Borisov and A. A. Kilin and I. S. Mamaev},
     title = {Integrability and nonintegrability of {sub-Riemannian} geodesic flows on {Carnot} groups},
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I. A. Bizyaev; A. V. Borisov; A. A. Kilin; I. S. Mamaev. Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 1, pp. 129-146. http://geodesic.mathdoc.fr/item/ND_2017_13_1_a8/