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

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

Russian journal of nonlinear dynamics, Tome 13 (2017) no. 1, pp. 129-146.

Résumé

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.

Détail

Keywords: sub-Riemannian geometry, first integrals.
Mots-clés : Carnot group, Poincaré map

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