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Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity

Autor
Baldoma, I.; Castejon, O.; Martinez-seara, Tere
Tipus d'activitat
Article en revista
Revista
Journal of dynamics and differential equations
Data de publicació
2013
Volum
25
Número
2
Pàgina inicial
335
Pàgina final
392
DOI
https://doi.org/10.1007/s10884-013-9297-2 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/20865 Obrir en finestra nova
URL
http://link.springer.com/article/10.1007%2Fs10884-013-9297-2 Obrir en finestra nova
Resum
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 ...
Citació
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.
Paraules clau
Exponentially small phenomena, Hopf-zero singularity, Singular perturbation theory, Splitting of separatrices
Grup de recerca
SD - Sistemes Dinàmics de la UPC

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