Journal of Mathematical Physics, Analysis, Geometry 2022, vol. 18, No 1, pp. 33-56   https://doi.org/10.15407/mag18.01.033     ( to contents , go back )

### Jacobi-Lie Hamiltonian Systems on Real Low-Dimensional Jacobi-Lie Groups and their Lie Symmetries

Department of Mathematics, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran

Gh. Haghighatdoost

Department of Mathematics, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran
E-mail: gorbanali@azaruniv.ac.ir

A. Rezaei-Aghdam

Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran
E-mail: rezaei-a@azaruniv.ac.ir

Received October 15, 2020, revised January 19, 2021.

Abstract

We study Jacobi-Lie Hamiltonian systems admitting VessiotGuldberg Lie algebras of Hamiltonian vector fields related to Jacobi structures on real low-dimensional Jacobi-Lie groups. Also, we find all possible examples of Jacobi-Lie Hamiltonian systems on real two- and three-dimensional Jacobi-Lie groups. Finally, we present Lie symmetries of Jacobi-Lie Hamiltonian systems on the real three-dimensional Lie group $SL(2, \mathbb{R}).$

Mathematics Subject Classification 2010: 34L15, 34L20, 35R10
Key words: Jacobi-Lie group, Jacobi manifold, Lie system, Jacobi-Lie Hamiltonian system, Lie symmetry