September  2008, 10(2&3, September): 323-347. doi: 10.3934/dcdsb.2008.10.323

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

1. 

Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain

Received  October 2006 Revised  July 2007 Published  June 2008

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.
Citation: I. Baldomá, Tere M. Seara. The inner equation for generic analytic unfoldings of the Hopf-zero singularity. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 323-347. doi: 10.3934/dcdsb.2008.10.323
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