The Hamiltonian Truncations of a Hamiltonian System

In a visinity of zero or infinity we consider Hamiltonian system of ordinary differential equations with m degrees of freedom. This Hamiltonian system is either a polynomial or a Laurent series. We study the truncated systems of the Hamiltonian system. The truncated system is asymptotically a first approximation of the initial system. We show that not each truncated system is a Hamiltonian one. Based on the Newton polyhedron of the Hamiltonian function, we give an algorithm for finding all truncated systems that are Hamiltonian systems. All previously know cases of Hamiltonian truncations of Hamiltonian systems may be found by the algorithm.