Discretization for St\"ackel system which conserves all constants of motion
Abstract:
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.