Now showing items 1-13 of 13

    • A survey of isochronous centers 

      Chavarriga Soriano, Javier; Sabatini, Marco (Edicions de la Universitat de Lleida, 1999)
    • A survey on the inverse integrating factor 

      García, I. A. (Isaac A.); Grau Montaña, Maite (Springer, 2010)
      The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles ...
    • Averaging methods of arbitrary order, periodic solutions and integrability 

      Giné, Jaume; Llibre, Jaume; Wu, Kesheng; Zhang, Xiang (Elsevier, 2016)
      In this paper we provide an arbitrary order averaging theory for higher dimensional periodic analytic differential systems. This result extends and improves results on averaging theory of periodic analytic differential ...
    • Centers for the Kukles homogeneous systems with odd degree 

      Giné, Jaume; Llibre, Jaume; Valls, Claudia (London Mathematical Society, 2015)
      For the polynomial differential system x˙ = −y, y˙ = x+Qn(x; y), where Qn(x; y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for ...
    • Formal inverse integrating factors and the nilpotent center problem 

      García, I. A. (Isaac A.) (World Scientific Publishing, 2016)
      We are interested in deepening knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields X. As formal integrability is not enough to ...
    • Integrability Conditions for Complex Homogeneous Kukles Systems 

      Giné, Jaume; Valls, Claudia (Atlantis and Taylor & Francis, 2018)
      In this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the ...
    • Integrability conditions for complex kukles systems 

      Giné, Jaume; Valls, Claudia (Taylor & Francis, 2017)
      In this paper, we provide necessary and sufficient conditions for the existence of local analytic first integrals for a seventh-parameter family of complex cubic systems called the complex Kukles systems.
    • Integrability conditions for Lotka–Volterra planar complex quintic systems 

      Giné, Jaume; Romanovski, Valery G. (Elsevier, 2010)
      In this paper we obtain necessary and sufficient integrability conditions at the origin for the Lotka–Volterra complex quintic systems which are linear systems perturbed by fifth degree homogeneous polynomials, i.e., we ...
    • Integrability conditions of a resonant saddle perturbed with homogeneous quintic nonlinearities 

      Giné, Jaume; Valls, Claudia (Springer, 2015)
      In this work we complete the integrability conditions (i.e. conditions for the existence of a local analytic first integral) for a family of a resonant saddle perturbed with homogeneous quintic nonlinearities studied in a ...
    • Integrability of complex planar systems with homogeneous nonlinearities 

      Fercec, Brigita; Giné, Jaume; Romanovski, Valery G.; Edneral, Victor F. (Elsevier, 2016)
      In this paper we obtain sufficient conditions for the existence of a local analytic first integral for a family of quintic systems having homogeneous nonlinearities. The family studied in this work is the largest one ...
    • 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, ...
    • Linearizability of planar polynomial Hamiltonian systems 

      Arcet, Barbara; Giné, Jaume; Romanovski, Valery G. (Elsevier, 2022)
      Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited and new results are presented. We give a new computational procedure to obtain the necessary and sufficient conditions for ...
    • 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 ...