Splitting of a small separatrix loop near the saddle-center bifurcation inarea-preserving maps

When the saddle-center bifurcation occurs in an analytic family of area-pre serving maps, a parabolic fixed point first appears at the origin and then this point bifurcates, creating an elliptic fixed point and a hyperbolic on e. Separatrices of the hyperbolic fixed point form a small loop around the elliptic point. In general the separatrices 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 pre-exponential factor. (C)2000 Elsevier Science B.V . All rights reserved.