 98646 V. Gelfreich
 Splitting of a small separatrix loop near the saddlecenter bifurcation
in areapreserving maps
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Oct 14, 98

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Abstract. When the saddlecenter bifurcation occurs in an analytic family of
areapreserving maps, first a parabolic fixed point appears at the origin
and then this point bifurcates, creating an elliptic and hyperbolic fixed
point. Separatrices of the hyperbolic fixed point form a small loop around
the elliptic point. In general the separatrices intersect transversaly and
the splitting is exponentially small with respect to the perturbation
parameter. We derive an asymptotic formula, which describes the
splitting, and study the properties of the preexponential factor.
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