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Exponentially small splitting of separatrices in the perturbed McMillan map

Author
Martin, P.; Sauzin, D.; Martinez-seara, M.
Type of activity
Journal article
Journal
Discrete and continuous dynamical systems. Series A
Date of publication
2011-10
Volume
31
Number
2
First page
301
Last page
372
DOI
https://doi.org/10.3934/dcds.2011.31.301 Open in new window
Repository
http://hdl.handle.net/2117/13218 Open in new window
URL
http://www.aimsciences.org/journals/home.jsp?journalID=1 Open in new window
Abstract
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...
Citation
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.
Keywords
McMillan map, asymptotic formula, exponentially small phenomena, splitting of separatrices
Group of research
SD - UPC Dynamical Systems

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