Now showing items 1-20 of 23

    • A Chebyshev criterion for Abelian integrals 

      Grau Montaña, Maite; Mañosas, Francesc; Villadelprat, Jordi (American Mathematical Society, 2010)
      We present a criterion that provides an easy sufficient condition in order that a collection of Abelian integrals has the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals ...
    • A survey of isochronous centers 

      Chavarriga Soriano, Javier; Sabatini, Marco (Edicions de la Universitat de Lleida, 1999)
    • 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 + ...
    • 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 ...
    • Evaluación del conocimiento estadístico en la formación inicial del profesorado 

      Estrada Roca, M. Asunción (Graó, 2007)
      Analizamos la educación estadística de los profesores en formación y presentamos un estudio de evaluación de los conocimientos estadísticos elementales de una muestra de 367 estudiantes de diferentes especialidades de ...
    • 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, ...
    • Lie symmetries and the center problem 

      Giné, Jaume (Shanghai Normal University & Wilmington Scientific Publisher, 2011)
      Abstract In this short survey we discuss the narrow relation between the center problem and the Lie symmetries. It is well known that an analytic vector field X having a non–degenerate center has a non–trivial analytic Lie ...
    • Periodic orbits in Hyperchaotic Chen systems 

      Maza Sabido, Susanna (Texas State University, 2015)
      In this work, we show a zero-Hopf bifurcation in a Hyperchaotic Chen system. Using averaging theory, we prove the existence of two periodic orbits bifurcating from the zero-Hopf equilibria located at the origin of ...