Planar quasi-homogeneous polynomial differential systems and their integrability

Belén García, Jaume Llibre, Jesús S. Pérez del Río

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22 Citations (Scopus)

Abstract

In this paper we study the quasi-homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree. Using this algorithm we obtain all quasi-homogeneous vector fields of degree 2 and 3.The quasi-homogeneous polynomial differential systems are Liouvillian integrable. In particular, we characterize all the quasi-homogeneous vector fields of degree 2 and 3 having a polynomial, rational or global analytical first integral. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)3185-3204
JournalJournal of Differential Equations
Volume255
Issue number10
DOIs
Publication statusPublished - 15 Nov 2013

Keywords

  • Analytic first integral
  • Polynomial first integral
  • Quasi-homogeneous polynomial differential system
  • Quasi-homogeneous polynomial vector field

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    García, B., Llibre, J., & Pérez del Río, J. S. (2013). Planar quasi-homogeneous polynomial differential systems and their integrability. Journal of Differential Equations, 255(10), 3185-3204. https://doi.org/10.1016/j.jde.2013.07.032