Liouvillian first integrals for a class of generalized Liénard polynomial differential systems

Jaume Llibre, Claùdia Valls

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3 Citations (Scopus)

Abstract

© 2016 Royal Society of Edinburgh. We study the existence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' =-g(x)-f(x)y, where f(x) = 3Q(x)Q'(x)P(x) + Q(x)2 P'(x) and g(x) = Q(x)Q'(x)(Q(x)2 P(x)2-1) with P,Q [x]. This class of generalized Liénard polynomial differential systems has the invariant algebraic curve (y + Q(x)P(x))2-Q(x)2 = 0 of hyperelliptic type.
Original languageEnglish
Pages (from-to)1195-1210
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume146
Issue number6
DOIs
Publication statusPublished - 1 Dec 2016

Keywords

  • Darboux polynomial
  • Liouvillian first integral
  • Liénard polynomial differential system
  • exponential factor
  • invariant algebraic curve

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