Discretization for St\"ackel system which conserves all constants of motion
A new discretization method for St\"ackel system is presented. This system is a wide class of integrable Hamiltonian systems. The given discrete system by the method conserves all of the constants of motion exactly as same as the original St\"ackel system. A combination of canonical transformations and an energy preserving discretization method with a variable step-size plays a important role in the discretization method.