Asymptotical Symmetrization of Hamilton Systems
We discuss a new algorithms of calculations of Hamiltonian normal form. A normal form of a Hamilton system has two main properties: a) Tailor expansion of the normal form has the simplest form; b) its linear part commutates with a nonlinear one. Property a is used for the normalization procedure. Property b) is used to build asymptotic solutions. For this purpose, instead of the normal form we define symmetrical form: a form satisfying property b). Symmetrization algorithm is reduced to sequential calculations of the quadrature in the approximation of each order and is essentially simpler than all the classical normalization procedures.