Now showing items 1-16 of 16

    • 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 ...
    • 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 ...
    • Center conditions for nilpotent cubic systems using Cherkas method 

      Giné, Jaume (Elsevier, 2016)
      In this work we study the center problem of a cubic polynomial differential system with nilpotent linear part. The analysis is based on the application of the Cherkas method to the Takens normal form. The study needs many ...
    • Center problem for systems with two monomial nonlinearities 

      Gasull i Embid, Armengol; Giné, Jaume; Torregrosa, Joan (American Institute of Mathematical Sciences, 2016)
      We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. ...
    • Center problem in the center manifold for quadratic differential systems in R^3 

      Giné, Jaume; Valls, Claudia (Elsevier, 2016)
      Using tools of computer algebra based on the Gröbner basis theory we derive conditions for the existence of a center on a local center manifold for fifteen seven-parameter families of quadratic systems on R 3. To obtain ...
    • Centers and isochronous centers for generalized quintic systems 

      Giné, Jaume; Llibre, Jaume; Valls, Claudia (Elsevier, 2015)
      In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d≥5 odd that in complex notation are ż=(λ+i)z(zz̄)d−52(Az5+Bz4z̄+Cz3z̄2+Dz2z̄3+Ezz̄4+Fz̄5), ...
    • Centers for generalized quintic polynomial differential systems 

      Giné, Jaume; Llibre, Jaume; Valls, Claudia (Rocky Mountain Mathematics Consortium, 2017)
      We classify the centers of polynomial differential systems in $R^2$ of odd degree $d \ge 5$, in complex notation, as $\dot{z} = iz + (z \bar z)^(d-5)/2(A z^5 + B z^4 \bar z + C z^3 \bar z^2 + D z^2 \bar z^3 + E z \bar z^4 ...
    • 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 ...
    • Cyclicity of a class of polynomial nilpotent center singularities 

      García, I. A. (Isaac A.); Shafer, Douglas S. (American Institute of Mathematical Sciences, 2016-04-01)
      In this work we extend techniques based on computational algebra for bounding the cyclicity of nondegenerate centers to nilpotent centers in a natural class of polynomial systems, those of the form $\dot x = y + P_{2m + ...
    • Integrability conditions of a resonant saddle in Liénard-like complex systems 

      Giné, Jaume; Valls, Claudia (Elsevier, 2016)
      We consider a complex differential system with a resonant saddle that remind the classical Liénard systems in the real plane. For such systems we determine the conditions of analytic integrability of the resonant saddle.
    • 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, ...
    • Reversible nilpotent centers with cubic homogeneous nonlinearities 

      Dukaric, Masa; Giné, Jaume; Llibre, Jaume (Elsevier, 2016)
      We provide 13 non--topological equivalent classes of global phase portraits in the Poincaré disk of reversible cubic homogeneous systems with a nilpotent center at origin, which complete the classification of the phase ...
    • The three-dimensional center problem for the zero-Hopf singularity 

      García, I. A. (Isaac A.); Valls, Claudia (American Institute of Mathematical Sciences, 2016-03-01)
      In this work we extend well-known techniques for solving the Poincar\'e-Lyapunov nondegenerate analytic center problem in the plane to the 3-dimensional center problem at the zero-Hopf singularity. Thus we characterize the ...