TITLE: The inner equation for generic analytic unfoldings
of the Hopf-zero singularity

AUTHORS:
Inmaculada Baldoma, T.M. Seara

Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya,
Diagonal 647, 08028 Barcelona, Spain

E-mails: immaculada.baldoma@upc.edu, Tere.M-Seara@upc.edu

ABSTRACT:

A classical problem in the study of the (conservative) unfoldings of the so
called Hopf-zero bifurcation, is the computation of the splitting of a
heteroclinic connection which exists in the symmetric normal form along the
z-axis. In this paper we derive the inner system associated to this singular
problem, which is independent on the unfolding parameter. We prove the
existence of two solutions of this system related with the stable and unstable
manifolds of the unfolding, and we give an asymptotic formula for their
difference.
We check that the results in this work agree with the ones obtained in
the regular case by the authors.