Now showing items 1-6 of 6

    • A note on Liouvillian first integrals and invariant algebraic curves 

      Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (Elsevier, 2013-02)
      In this work we study the existence and non-existence of finite invariant algebraic curves for a complex planar polynomial differential system having a Liouvillian first integral.
    • Integrability of Lotka-Volterra planar complex cubic systems 

      Dukaric, Masa; Giné, Jaume (World Scientific, 2016)
      In this paper we study the Lotka-Volterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, ...
    • Integrability of planar polynomial differential systems through linear differential equations 

      Giacomini, Héctor; Giné, Jaume; Grau Montaña, Maite (Rocky Mountain Mathematics Consortium, 2006)
      In this work we consider rational ordinary differential equations dy/dx = Q(x, y)/P(x, y), with Q(x, y) and P(x, y) coprime polynomials with real coefficients. We give a method to construct equations of this type for ...
    • 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 ...
    • The center problem for a 2:-3 resonant cubic Lotka–Volterra system 

      Dolićanin, Diana; Giné, Jaume; Oliveira, Regilene; Romanovski, Valery G. (Elsevier, 2013)
      In this paper we obtain conditions on the coefficients of a cubic Lotka–Volterra system of the form equation(1) x=x(2-a20x2-a11xy-a02y2), ẏ=y(-3+b20x2+b11xy+b02y2), which fulfillment yields the existence in a ...