Exponentially small splitting of separatrices in the perturbed McMillan map
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hdl:2117/13218
Tipus de documentArticle
Data publicació2011-10
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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 quantities related to
the splitting, namely the Lazutkin invariant and the area of the lobe between
two consecutive primary homoclinic points. Complex matching techniques are
in the core of this work. The coe cients involved in the expansion have a
resurgent origin, as shown in
CitacióMartín, 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.
ISSN1078-0947
Versió de l'editorhttp://www.aimsciences.org/journals/home.jsp?journalID=1
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