Jacobi-Lie systems: Fundamentals and low-dimensional classification

الأصل · EN

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. 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 R². Our results shall be illustrated through examples of physical and mathematical interest.