Exponentially small splitting of separatrices in the perturbed McMillan map
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hdl:2117/7381
Tipus de documentReport de recerca
Data publicació2009-12
Condicions d'accésAccés obert
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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 fixed 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 coefficients
involved in the expansion have a resurgent origin, as shown in
[MSS08].
Forma part[prepr200914MarSMS]
URL repositori externhttp://www.ma1.upc.edu/recerca/preprints/2009/prepr200904seara.pdf
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resurgence.pdf | 451,3Kb | Visualitza/Obre |