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Generalized pseudo-Hamiltonian normal forms (GPHNF) and an effective methodof obtaining them are introduced for two-dimensional systems of autonomous ODEswith a Hamiltonian quasi-homogeneous unperturbed part of an arbitrary degree.The terms that can be additionally eliminated in a GPHNF are constructivelydistinguished, and it is shown that after removing them GPHNF becomes ageneralized normal form (GNF). By using the introduced method, all the GNFs areobtained in cases where the unperturbed part of the system is Hamiltonian andhas monomial components, which allowed to generalize some results by Takens,Baider and Sanders, as well as Basov et al.

Generalized Normal Forms of Two-Dimensional Autonomous Systems with a Hamiltonian Unperturbed Part