Singular Reduction of Symmetries

• 作 者: J(e)drzej(S)niatycki;
• 出 处: The Third International Conference on Dynamics,Vibration and
• 发表日期: 2010年期

　　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.