Polynomial and rational first integrals for planar quasi{homogeneous polynomial differential systems

Jaume Giné; Maite Grau; Jaume Llibre

doi:https://doi.org/10.3934/dcds.2013.33.4531

Polynomial and rational first integrals for planar quasi{homogeneous polynomial differential systems

Jaume Giné, Maite Grau, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

14 Citations (Scopus)

Abstract

In this paper we find necessary and suficient conditions in or- der that a planar quasi{homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi{ homogeneous polynomial differential system can be transformed into a differen- tial system of the form u· = uf(v), v· = g(v) with f(v) and g(v) polynomials, and vice versa.

Original language	English
Pages (from-to)	4531-4547
Journal	Discrete and Continuous Dynamical Systems
Volume	33
Issue number	10
DOIs	https://doi.org/10.3934/dcds.2013.33.4531
Publication status	Published - 1 Oct 2013

Keywords

Integrability problem
Polynomial first integral
Quasi{homogeneous polynomial differential equations
Rational first integral

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N2 - In this paper we find necessary and suficient conditions in or- der that a planar quasi{homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi{ homogeneous polynomial differential system can be transformed into a differen- tial system of the form u· = uf(v), v· = g(v) with f(v) and g(v) polynomials, and vice versa.

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KW - Quasi{homogeneous polynomial differential equations

KW - Rational first integral

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Polynomial and rational first integrals for planar quasi{homogeneous polynomial differential systems

Abstract

Keywords

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