Vladimir V. Basov
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics,
Differential Equations Department
Leonid S. Mikhlin
Universitetsky prospekt, 28, 198504, Peterhof, Saint-Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics, Differential Equations Department
Two-dimensional autonomous systems of ODE with linear-cubic polynomial as the unperturbed part, which is linearly equivalent to a quasi-homogeneous polynomial, are reduced by formal invertible transformation to generalized normal forms. All structures of generalized normal forms are obtained by a constructive method. In addition, a classification of systems whith a quasi-homogeneous polynomial of the second generalized degree with weight (1,3) in the unperturbed part, was presented.