The generalized Liénard polynomial differential systems x'=y, y'=-g(x)-f(x)y with degg=degf+1 are not Liouvillian integrable

Jaume Llibre, Clàudia Valls

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4 Citations (Scopus)

Abstract

© 2014 Elsevier Masson SAS. We prove the nonexistence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x'=y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that degg=degf+1.
Original languageEnglish
Pages (from-to)214-227
JournalBulletin des Sciences Mathematiques
Volume139
Issue number2
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Darboux polynomials
  • Exponential factors
  • Liouvillian first integrals
  • Liénard polynomial differential systems

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