Vladimir V. Basov
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics,
Differential Equations Department
Artur S. Vaganyan
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics,
Differential Equations Department
Equivalence of Hamiltonian systems in the neighborhood of a critical point relatively to the group
of formal canonical transformations is considered.
Definitions of metanormal and normal forms of a Hamiltonian system that do not require restrictions
on the unperturbed part of the Hamiltonian and a method of their finding are introduced.
Relationships between the introduced Hamiltonian normal forms
and the normal forms of Hamiltonian systems defined by A.D. Bruno and K.R. Meyer are studied.
Hamiltonian normal forms for real single degree of freedom Hamiltonian systems are obtained in the case
when the unperturbed part of the Hamiltonian is monomial and in the case
when the unperturbed part of the Hamiltonian is an irreducible binomial with coprime indices.