First Integrals of a Cubic System of Differential Equations

Zhibek Kadyrsizova, Valery G. Romanovski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study polynomial systems of differential equations of the form X = x+p(x,y), y = -3y+q(x,y), (1) where p(x,y) and q(x,y) are homogeneous polynomials of degree three. In [1] the linearizability problem for this system has been studied. In many cases considered in [1] the construction of linearizing transformations requires knowledge of first integrals. In [2] it has been proved that such integrals exist. In the present paper we find the explicit expressions for the integrals. It allows to obtain the explicit formulas for the corresponding linearizing transformations of [1].

Original languageEnglish
Title of host publication7th International Summer School/Conference "Let's Face Chaos Through Nonlinear Dynamics" - Dedicated to the 65th Birthday of Professor Giulio Casati
EditorsValery G. Romanovski, Marko Robnik
PublisherAmerican Institute of Physics Inc.
Pages104-111
Number of pages8
ISBN (Electronic)9780735406070
DOIs
Publication statusPublished - Jan 1 2008
Externally publishedYes
Event7th International Summer School/Conference "Let's Face Chaos Through Nonlinear Dynamics" - Maribor, Slovenia
Duration: Jun 29 2008Jul 13 2008

Publication series

NameAIP Conference Proceedings
Volume1076
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference7th International Summer School/Conference "Let's Face Chaos Through Nonlinear Dynamics"
Country/TerritorySlovenia
CityMaribor
Period6/29/087/13/08

Keywords

  • integrability
  • ordinary differential equations
  • the center and linearizability problems

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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