Paper_with_Jinrong2.pdf (965.5 kB)
A note about integrable systems on low-dimensional Lie groups and Lie algebras
journal contribution
posted on 2019-07-22, 09:09 authored by Alexey V. Bolsinov, Jinrong BaoThe 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. We also give normal forms for left-invariant Riemannian and sub-Riemannian metrics on 3-dimensional Lie groups focusing on the case of solvable groups, as the cases of SO(3) and SL(2) have been already extensively studied. Our description is explicit and is given in global coordinates on G which allows one to easily obtain parametric equations of geodesics in quadratures.
History
School
- Science
Department
- Mathematical Sciences
Published in
Regular and Chaotic DynamicsVolume
24Issue
3Pages
266 - 280Citation
BOLSINOV, A.V. and BAO, J., 2019. A note about integrable systems on low-dimensional Lie groups and Lie algebras. Regular and Chaotic Dynamics, 24 (3), pp.266-280.Publisher
© Pleiades Publishing, Ltd.Version
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2018-10-20Publication date
2019-06-03Notes
This a preprint of the Work accepted for publication in Regular and Chaotic Dynamics, © 2019 Pleiades Publishing, Ltd. The definitive published version is available at https://doi.org/10.1134/S156035471903002X. The publisher's website is at: http://pleiades.online/ISSN
1560-3547eISSN
1468-4845Publisher version
Language
- en