A Note about Integrable Systems on Low-dimensional Lie Groups and Lie Algebras

被引:0
|
作者
Alexey Bolsinov
Jinrong Bao
机构
[1] Loughborough University,School of Mathematics
[2] Moscow State University,Faculty of Mechanics and Mathematics
来源
关键词
Integrable systems; Lie groups; geodesic flow; left-invariant metric; sub-Riemannian structure; 37J35; 53B50; 70H06; 70S10;
D O I
暂无
中图分类号
学科分类号
摘要
The goal of the paper is to explain why any left-invariant Hamiltonian system on (the cotangent bundle of) a 3-dimensonal Lie group G is Liouville integrable. We derive this property from the fact that the coadjoint orbits of G are two-dimensional so that the integrability of left-invariant systems is a common property of all such groups regardless their dimension.
引用
收藏
页码:266 / 280
页数:14
相关论文
共 50 条
  • [1] A Note about Integrable Systems on Low-dimensional Lie Groups and Lie Algebras
    Bolsinov, Alexey
    Bao, Jinrong
    [J]. REGULAR & CHAOTIC DYNAMICS, 2019, 24 (03): : 266 - 280
  • [2] Integrable Hamiltonian systems on low-dimensional Lie algebras
    Korotkevich, A. A.
    [J]. SBORNIK MATHEMATICS, 2009, 200 (11-12) : 1731 - 1766
  • [3] A note on optimal systems of certain low-dimensional Lie algebras
    Singh, Manjit
    Gupta, Rajesh Kumar
    [J]. INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2021, 22 (02) : 135 - 144
  • [4] LOW-DIMENSIONAL COHOMOLOGY GROUPS OF THE LIE ALGEBRAS W(a, b)
    Gao, Shoulan
    Jiang, Cuipo
    Pei, Yufeng
    [J]. COMMUNICATIONS IN ALGEBRA, 2011, 39 (02) : 397 - 423
  • [5] Low-dimensional filiform Lie algebras
    Gomez, JR
    Jimenez-Merchan, A
    Khakimdjanov, Y
    [J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1998, 130 (02) : 133 - 158
  • [6] Contractions of low-dimensional Lie algebras
    Nesterenko, Maryna
    Popovych, Roman
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (12)
  • [7] LOW-DIMENSIONAL REAL LIE-ALGEBRAS
    TURKOWSKI, P
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1988, 29 (10) : 2139 - 2144
  • [8] Realizations of real low-dimensional Lie algebras
    Popovych, RO
    Boyko, VM
    Nesterenko, MO
    Lutfullin, MW
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (26): : 7337 - 7360
  • [9] Classification of controllable systems on low-dimensional solvable lie groups
    Sachkov Yu.L.
    [J]. Sachkov, Yu.L., 2000, Kluwer Academic/Plenum Publ Corp, New York, NY, United States (06) : 159 - 217
  • [10] Lie Algebras and Integrable Systems
    Zhang Yu-Feng
    Mei Jian-Qin
    [J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2012, 57 (06) : 1012 - 1022