Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity
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In this paper we prove the breakdown of a heteroclinic connection in the analytic versal unfoldings of the generic Hopf-zero singularity in an open set of the parameter space. 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 corresponding stable and unstable one-dimensional manifolds which is given by an exponentially small function in the perturbation parameter. Our result applies both for conservative and dissipative unfoldings
CitationBaldoma, I.; Castejon, O.; Martinez-seara, M. Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity. "Journal of dynamics and differential equations", 2013, vol. 25, núm. 2, p. 335-392.