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

Jaume Giné, Maite Grau, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Pages (from-to)4531-4547
JournalDiscrete and Continuous Dynamical Systems
Volume33
Issue number10
DOIs
Publication statusPublished - 1 Oct 2013

Keywords

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

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