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Presence of symmetries in Hamiltonian systems simplifies the task of solving equations of motion.If the action of the symmetry group G on a symplectic manifold (P,ω) is free and proper the space P/G of G-orbits in P is a Poisson manifold and the orbit map: p : P → P / G is a locally trival fibration.If the action of G on P is proper but not free.the orbit space P/G is not a manifold but a smoothly stratified space.One can recover all the structure of P / G from the structure of the ring C∞(P)G of smooth G-invariant functions on P.