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Keywords
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Jacobi–Lie group, Jacobi manifold, Lie system, Jacobi–Lie
Hamiltonian system, Lie symmetry
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Abstract
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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 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, R).
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