Classification of Two-dimensional Homogeneous Cubic Systems of Ordinary Differential Equations without a General Multiplier
Author(s):
Vladimir V. Basov
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics,
Differential Equations Department
vlvlbasov@rambler.ru
Evgenia Fedorova
Saint Petersburg State Technological University of Plant Polymers,
The Faculty of Industrial Heat Power Engineering, Higher Mathematics Department
fev.math@gmail.com
Abstract:
We consider two-dimensional real autonomous systems of ODE with right-hand sides as
vector homogeneous polynomials of the third order whose components do not have a
general multiplier.
In each class of equivalency with respect to linear transformations
we mark out in the right-hand side the canonical form --- the simplest polynomial used
as an unperturbed part in a formal or analytical system which has to be reduced
to a generalized normal form.
Conditions on coefficients of a given system and the linear transformation
reducing the system under these conditions to a system with given canonical form are presented.
References:
- V. V. Basov and E. V. Fedorova. Classification of Two-dimensional Homogeneous Cubic Systems of Ordinary Differential Equations under the Presence of a General multiplier: I // Differential Equations and Control Processes (Electronic Journal: http://www. math. spbu. ru/diffjournal), No. 2, 2012, pp. 218--276
- V. V. Basov and E. V. Fedorova. Classification of Two-dimensional Homogeneous Cubic Systems of Ordinary Differential Equations under the Presence of a General multiplier: II // Differential Equations and Control Processes (Electronic Journal: http://www. math. spbu. ru/diffjournal), No. 3, 2012, pp. 139--167
- V. V. Basov and A. V. Skitovich. A Generalized Normal Form and Formal Equivalence of Two-Dimensional Systems with Quadratic Zero Approximation: I // Differential Equations, Vol. 39, No. 8, 2003, pp. 1067--1081. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 8, 2003, pp. 1016--1029. Original Russian Text Copyright c 2003 by Basov, Skitovich
- V. V. Basov and E. V. Fedorova. Two-dimensional Real Systems of Ordinary Differential Equations with Quadratic Unperturbed Parts: Classification and Degenerate Generalized Normal Forms // Differential Equations and Control Processes (Electronic Journal: http://www. math. spbu. ru/diffjournal), No. 4, 2010, pp. 49--85
