# Jacobi-Lie Hamiltonian systems on real low-dimensional Jacobi-Lie groups and their Lie symmetries

## TL;DR

This paper investigates Jacobi-Lie Hamiltonian systems on low-dimensional Jacobi-Lie groups, exploring their Lie symmetries and providing concrete examples on two- and three-dimensional groups.

## Contribution

It introduces the study of Jacobi-Lie Hamiltonian systems on low-dimensional groups and identifies their Lie symmetries with explicit examples.

## Key findings

- Examples of Jacobi-Lie Hamiltonian systems on 2D and 3D groups.
- Identification of Lie symmetries for these systems.
- Analysis of Hamiltonian vector fields related to Jacobi structures.

## Abstract

We study Jacobi-Lie Hamiltonian systems admitting Vessiot-Guldberg Lie algebras of Hamiltonian vector fields related to Jacobi structures on real low-dimensional Jacobi-Lie groups. Also, we find some 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 some three-dimensional real Jacobi-Lie groups.