Analytic integrability of a class of planar polynomial differential systems

Jaume Llibre, Claudia Valls

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1 Citation (Scopus)


Copyright © DCDSB. 2015. In this paper we find necessary and sufficient conditions in order that the differential systems of the form x. = xf(y), y. = g(y), with f and g polynomials, have a first integral which is analytic in the variable x and meromorphic in the variable y. We also characterize their analytic first integrals in both variables x and y. These polynomial differential systems are important because after a convenient change of variables they contain all quasi-homogeneous polynomial differential systems in ℝ2.
Original languageEnglish
Pages (from-to)2657-2661
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number8
Publication statusPublished - 1 Jan 2015


  • Analytic first integrals
  • Planar polynomial systems
  • Pseudo-meromorphic first integrals
  • Quasi-homogeneous polynomial differential systems


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