Generalized Normal Forms of Systems with a Hamiltonian Unperturbed Part
Author(s):
A. S. Vaganyan
Saint-Petersburg State University,
Faculty of Math.and Mech.
Department of Differential Equations
armay@yandex.ru
Abstract:
In this article the question of finding the structures
of generalized normal forms of systems
with a Hamiltonian quasi-homogeneous unperturbed part
and a non-Hamiltonian perturbation is considered.
Our approach is based on the Belitskii method
and uses the idea due to A. Baider and J. Sanders
of decomposing the perturbation into "Hamiltonian" and "non-Hamiltonian" parts.
As examples of applications of the method,
results obtained earlier by the author in collaboration with V. Basov
for the two-dimensional case are presented,
and a generalization of the F.Takens' theorem
on the normal form of a system with a nilpotent unperturbed part
to the case of an arbitrary number of Jordan blocks is given.
Keywords
- Hamiltonian systems
- nilpotent unperturbed part
- normal forms
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