Breakdown of heteroclinic orbits for analytic unfoldings of the hopf-zero singularity. The singular case

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Defense date2011
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Abstract
In this paper we prove the breakdown of an heteroclinic connection in
the analytic versal unfoldings of the generic Hopf-Zero singularity. This
heteroclinic orbit appears at any order if one performs the normal form
around the origin, therefore it is a phenomenon \beyond all orders". In
this paper we provide a formula for the distance between the correspond-
ing stable and unstable one dimensional manifolds which is given by an
exponentially small function in the perturbation parameter. Our result
applies both for conservative unfoldings and for dissipative ones in some
open regions of the parameter plane
CitationBaldomá, I.; Castejón, O.; Martínez-Seara, M. "Breakdown of heteroclinic orbits for analytic unfoldings of the hopf-zero singularity. The singular case". 2011.
URL other repositoryhttp://www.ma1.upc.edu/recerca/preprints/2011/
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