• On planar polynomial vector fields with elementary first integrals 

      Christopher, Colin; Pantazi, Chara; Llibre Saló, Jaume; Walcher, Sebastian (2019-10-05)
      Article
      Accés obert
      We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. ...
    • Some inverse problems 

      Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (2011-07-06)
      Report de recerca
      Accés restringit per política de l'editorial
      The Darboux theory of integrability for planar polynomial di®erential equations is a classical ¯eld, with connections to Lie symmetries, di®erential algebra and other areas of mathematics. In the present paper we introduce ...
    • Three-dimensional Lotka–Volterra systems with 3:-1:2-resonance 

      Aziz, Waleed; Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara (2021-08)
      Article
      Accés obert
      We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:- 1:2)-resonance. We give necessary and sufficient conditions on the parameters of ...