Now showing items 1-8 of 8

    • Analytic nilpotent centers as limits of nondegenerate centers revisited 

      García, I. A. (Isaac A.); Giacomini, Héctor; Giné, Jaume; Llibre, Jaume (Elsevier, 2016-04-25)
      We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré--Liapunov method to detect centers with purely imaginary ...
    • Effective construction of Poincaré-Bendixson regions 

      Gasull, Armengol; Giacomini, Héctor; Grau Montaña, Maite (Shanghai Normal University & Wilmington Scientific Publisher, 2017)
      This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal curves, that ...
    • 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 ...
    • The inverse integrating factor and the Poincaré map 

      García, I. A. (Isaac A.); Giacomini, Héctor; Grau Montaña, Maite (American Mathematical Society, 2010)
      This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ...
    • The null divergence factor 

      Chavarriga Soriano, Javier; Giacomini, Héctor; Giné, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques, 1997)
      Let (P, Q) be a C 1 vector field defined in a open subset U ⊂ R2 . We call a null divergence factor a C 1 solution V (x, y) of the equation P ∂V + Q ∂V = ∂P + ∂Q V . In previous works ∂x ∂y ∂x ∂y it has been ...
    • The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems 

      Giacomini, Héctor; Giné, Jaume; Llibre, Jaume (Elsevier, 2006)
      In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov ...
    • The role of algebraic solutions in planar polynomial differential systems 

      Giacomini, Héctor; Giné, Jaume; Grau Montaña, Maite (Cambridge University Press, 2007)
      We study a planar polynomial differential system, given by . We consider a function , where gi(x) are algebraic functions of with ak(x) and algebraic functions, A0(x,y) and A1(x,y) do not share any common factor, h2(x) is ...
    • Transversal conics and the existence of limit cycles 

      Giacomini, Héctor; Grau Montaña, Maite (Elsevier, 2015)
      This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal conics. We present ...