A Lie system is a system of differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields, a Vessiot-Guldberg Lie algebra. In this paper (**arXiv:11412.0300**) we define and analyze Lie systems possessing a Vessiot-Guldberg Lie algebra of Hamiltonian vector fields relative to a Jacobi manifold, the hereafter called Jacobi-Lie systems. We classify Jacobi-Lie systems on R and R^2. Our results shall be illustrated through examples of physical and mathematical interest.

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