• Breakdown of a 2D heteroclinic connection in the hopf-zero singularity (I) 

      Baldomá Barraca, Inmaculada; Castejón Company, Oriol; Martínez-Seara Alonso, M. Teresa (2018-10-01)
      Article
      Accés obert
      In this paper we study a beyond all orders phenomenon which appears in the analytic unfoldings of the Hopf-zero singularity. It consists in the breakdown of a two-dimensional heteroclinic surface which exists in the truncated ...
    • Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (II): The generic case 

      Baldomá Barraca, Inmaculada; Castejón Company, Oriol; Martínez-Seara Alonso, M. Teresa (2018-04-17)
      Article
      Accés obert
      In this paper, we prove the breakdown of the two-dimensional stable and unstable manifolds associated to two saddle-focus points which appear in the unfoldings of the Hopf-zero singularity. The method consists in obtaining ...
    • Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity 

      Baldomá Barraca, Inmaculada; Martínez-Seara Alonso, M. Teresa (2004)
      Article
      Accés obert
      In this paper we study the exponentially small splitting of a heteroclinic orbit in some unfoldings of the central singularity also called Hopf-zero singularity. The fields under consideration are of the form: dx dτ = ...