Department of Applied Mathematics and Physics
Graduate School of Informatics, Kyoto University,
Kyoto 606-8501, JAPAN
E-mail: minesaki@amp.i.kyoto-u.ac.jp

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.