Now showing items 1-4 of 4

    • 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 ...
    • 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 ...