Splitting of a Small Separatrix Loop near the Saddle-center Bifurcation in Area-preserving Maps
نویسنده
چکیده
When the saddle-center bifurcation occurs in an analytic family of area-preserving maps, rst a parabolic xed point appears at the origin and then this point bi-furcates, creating an elliptic xed point and a hyperbolic one. Separatrices of the hyperbolic xed point form a small loop around the elliptic point. In general the sep-aratrices intersect transversely 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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