• Invariant algebraic surfaces of polynomial vector fields in dimension three 

      Kruff, Niclas; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (Springer, 2021-01-01)
      Article
      Accés obert
      We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincaré from dimension ...
    • Morphisms and inverse problems 

      Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (2011-11-03)
      Report de recerca
      Accés obert
      In order to investigate polynomial vector ¯elds admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the a±ne plane. In particular, such morphisms may be used to remove ...
    • Morphisms and inverse problems for Darboux integrating factors 

      Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (2013-12)
      Article
      Accés obert
      Polynomial vector fields which admit a prescribed Darboux integrat- ing factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane ...
    • 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 ...