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

被引：15
|
作者：
Bizyaev, Ivan A. [1 ]
Borisov, Alexey V. [1 ,2 ]
Kilin, Alexander A. [1 ]
Mamaev, Ivan S. [3 ]
机构：
[1] Udmurt State Univ, Ul Univ Skaya 1, Izhevsk 426034, Russia
[2] Natl Res Nucl Univ MEPhI, Kashirskoe Sh 31, Moscow 115409, Russia
[3] Izhevsk State Tech Univ, Ul Studencheskaya 7, Izhevsk 426069, Russia
来源：
REGULAR & CHAOTIC DYNAMICS | 2016年 / 21卷 / 06期
基金：
俄罗斯科学基金会;
关键词：
sub-Riemannian geometry; Carnot group; Poincare map; first integrals; MILLS CLASSICAL MECHANICS; HAMILTONIAN-SYSTEMS; POTENTIALS; DISTRIBUTIONS;
D O I：
10.1134/S1560354716060125
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 Poincar, 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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页码：759 / 774
页数：16
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