Symplectification of Truncated Maps for Hamiltonian Systems

Serge N. Andrianov
St.Petersburg State University, Bibliotechnaja pl. 2,
St.Petersburg 198904 RUSSIA


The time-displacement operator for Hamiltonian dynamical systems is a symplectic transformation - Lie maps. Any trancated Lie map (Lie approximant) loses the very important syplectic property. In this report a method of correction this truncated map is suggested. The matrix representation for desired symplectic map is calculated in the symbolic form. The symplectification conditions have the form of symple linear algebraic equations. The symbolic solution of these equation are prepared in advanced and are stored in a corresponding database. This approach allows us to simplify calculation process for dynamical systems evolution, in particular, for long time evolution.


IMACS ACA'98 Electronic Proceedings