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Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity

Author
Baldoma, I.; Castejon, O.; Martinez-seara, M.
Type of activity
Journal article
Journal
Journal of dynamics and differential equations
Date of publication
2013
Volume
25
Number
2
First page
335
Last page
392
DOI
https://doi.org/10.1007/s10884-013-9297-2 Open in new window
Repository
http://hdl.handle.net/2117/20865 Open in new window
URL
http://link.springer.com/article/10.1007%2Fs10884-013-9297-2 Open in new window
Abstract
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 ...
Citation
Baldoma, 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.
Keywords
Exponentially small phenomena, Hopf-zero singularity, Singular perturbation theory, Splitting of separatrices
Group of research
SD - UPC Dynamical Systems

Participants