Now showing items 1-8 of 8

    • Analytic integrability inside a family of degenerate centers 

      Algaba, Antonio; Checa, Isabel; García, Cristóbal; Giné, Jaume (Elsevier, 2016)
      In this paper we study the analytic integrability around the origin inside a family of degenerate centers or perturbations of them. For this family analytic integrability does not imply formal orbital equivalence to a ...
    • Analytic integrability of some examples of degenerate planar vector fields 

      Algaba, Antonio; García, Cristóbal; Giné, Jaume (Springer, 2016)
      This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate ...
    • Geometric criterium in the center problem 

      Algaba, Antonio; García, Cristóbal; Giné, Jaume (Springer Basel, 2016-10)
      In this paper we use a geometric criterium based in the classical method of the construction of Lyapunov functions to determine if a differential system has a focus or a center at a singular point. This criterium is proved ...
    • Nilpotent centres via inverse integrating factors 

      Algaba, Antonio; García, Cristóbal; Giné, Jaume (Cambridge University Press, 2016-10)
      In this paper we are interested in the nilpotent center problem of planar analytic monodromic vector fields. It is known that the formal integrability is not enough to characterize such centers. More general objects are ...
    • On the extensions of the Darboux theory of integrability 

      Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (IOP Publishing, 2013)
      Recently some extensions of the classical Darboux integrability theory to autonomous and non-autonomous polynomial vector fields were completed. The classical Darboux integrability theory and its recent extensions are based ...
    • Polynomial and rational first integrals for planar homogeneous polynomial differential systems 

      Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (Universitat Autònoma de Barcelona, 2014)
      In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic ...
    • Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems 

      Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (American Institute of Mathematical Sciences, 2013-10)
      In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous ...
    • Weierstrass integrability of differential equations 

      Giné, Jaume; Grau Montaña, Maite (Elsevier, 2010)
      The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or ...