Publicacions Matemàtiques

Polynomial and rational first integrals for planar homogeneous polynomial differential systems

Jaume Giné, Maite Grau, and Jaume Llibre

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Abstract

In this paper we find necessary and sufficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic homogeneous polynomial differential systems.

Article information

Source
Publ. Mat., Volume EXTRA (2014), 255-278.

Dates
First available in Project Euclid: 19 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.pm/1400505236

Mathematical Reviews number (MathSciNet)
MR3211837

Zentralblatt MATH identifier
1310.34003

Subjects
Primary: 34C05: Location of integral curves, singular points, limit cycles 34A34: Nonlinear equations and systems, general 34C20: Transformation and reduction of equations and systems, normal forms

Keywords
First integral polynomial differential equations integrability problem

Citation

Giné, Jaume; Grau, Maite; Llibre, Jaume. Polynomial and rational first integrals for planar homogeneous polynomial differential systems. Publ. Mat. EXTRA (2014), 255--278. https://projecteuclid.org/euclid.pm/1400505236


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