Now showing items 1-4 of 4

    • Averaging theory at any order for computing periodic orbits 

      Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (Elsevier, 2013-05)
      We provide a recurrence formula for the coefficients of the powers of ε in the series expansion of the solutions around ε=0 of the perturbed first-order differential equations. Using it, we give an averaging theory at any ...
    • Non-existence of limit cycles for planar vector fields 

      Giné, Jaume (Texas State University. Department of Mathematics, 2014)
      This article presents sufficient conditions for the non-existence of limit cycles for planar vector fields. Classical methods for the nonexistence of limit cycles are connected with the theory developed here.
    • The cubic polynomial differential systems with two circles as algebraic limit cycles 

      Giné, Jaume; Llibre, Jaume; Valls, Claudia (Walter de Gruyter GmbH, 2018)
      In this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles.
    • 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 ...