Finding the Incomplete Belitskii Normal Form of a Hamiltonian System

We suggest an efficient method for finding the incomplete Belitskii normal form of a Hamiltonian system with many degrees of freedom and with a quasihomogeneous unperturbed part of special form. In particular, we obtain closed-form expressions for the incomplete Belitskii normal forms of two-degree-of-freedom Hamiltonian systems with unperturbed Hamiltonian of the form $h_1x_1^{l_1}y_1^{m_1}+h_2x_2^{l_2}y_2^{m_2}$.