Now showing items 1-8 of 8

    • A new sufficient condition in order that the real Jacobian conjecture in R2 holds 

      Giné, Jaume; Llibre, Jaume (Elsevier, 2021)
      Let F = (f, g) : R2 → R2 be a polynomial map such that det(DF (x, y)) is nowhere zero and F (0, 0) = (0, 0). In this work we give a new sufficient condition for the injectivity of F . We also state a conjecture when ...
    • Center cyclicity for some nilpotent singularities including the Z2-equivariant class 

      García, I. A. (Isaac A.) (World Scientific Publishing, 2021-10-20)
      This work concerns with polynomial families of real planar vector fields having a monodromic nilpotent singularity. The families considered are those for which the centers are characterized by the existence of a formal ...
    • Center cyclicity of a family of quartic polynomial differential system 

      García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Springer, 2016-09-01)
      In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as z = i z + z z (A z^2 + B z z + C z^2 ), where A,B,C. We give an upper bound for the cyclicity of any ...
    • Center cyclicity of Lorenz, Chen and Lü systems 

      García, I. A. (Isaac A.); Maza Sabido, Susanna; Shafer, Douglas S. (Elsevier, 2018-11-09)
      This work provides upper bounds on the cyclicity of the centers on center manifolds in the well-known Lorenz family, and also in the Chen and Lü families. We prove that at most one limit cycle can be made to bifurcate from ...
    • Center problem with characteristic directions and inverse integrating factors 

      García, I. A. (Isaac A.); Giné, Jaume (Elsevier, 2022)
      We consider the center-focus problem for analytic families of planar vector fields having a monodromic singularity with characteristic directions. We give a method to compute the center conditions of the family provided ...
    • Examples of center cyclicity bounds using the reduced Bautin depth 

      García, I. A. (Isaac A.) (American Mathematical Society, 2017-09-01)
      There is a method for bounding the cyclicity of nondegenerate monodromic singularities of polynomial planar families of vector fields Xλ which can work even in case that the Poincar´e first return map has associated a ...
    • The cyclicity of polynomial centers via the reduced bautin depth 

      García, I. A. (Isaac A.) (American Mathematical Society, 2016)
      We describe a method for bounding the cyclicity of the class of monodromic singularities of polyn omial planar families of vector fields X λ with an analytic Poincar e first return map having a polynomial Bautin ideal B ...
    • The Hopf cyclicity of the centers of a class of quintic polynomial vector fields 

      García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Elsevier, 2015-01-20)
      We consider families of planar polynomial vector fields having a singularity with purely imaginary eigenvalues for which a basis of its Bautin ideal B is known. We provide an algorithm for computing an upper bound of the ...