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Exponentially small splitting of separatrices in the perturbed McMillan map

Autor
Martin, P.; Sauzin, D.; Martinez-seara, Tere
Tipus d'activitat
Article en revista
Revista
Discrete and continuous dynamical systems. Series A
Data de publicació
2011-10
Volum
31
Número
2
Pàgina inicial
301
Pàgina final
372
DOI
https://doi.org/10.3934/dcds.2011.31.301 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/13218 Obrir en finestra nova
URL
http://www.aimsciences.org/journals/home.jsp?journalID=1 Obrir en finestra nova
Resum
The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic xed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantitie...
Citació
Martín, P.; Sauzin, D.; Martínez-Seara, M. Exponentially small splitting of separatrices in the perturbed McMillan map. "Discrete and continuous dynamical systems. Series A", Octubre 2011, vol. 31, núm. 2, p. 301-372.
Paraules clau
McMillan map, asymptotic formula, exponentially small phenomena, splitting of separatrices
Grup de recerca
SD - Sistemes Dinàmics de la UPC

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