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

被引：14

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.

引用

页码：759 / 774

页数：16

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