BEYOND ALL ORDERS - SINGULAR PERTURBATIONS IN A MAPPING

We consider a family of q-dimensional (q > 1), volume-preserving maps depending on a small parameter-epsilon. As epsilon --> 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for small epsilon the heteroclinic connection breaks up and that the splitting between its components scales with epsilon like epsilon(gamma) exp[-beta/epsilon]. We estimate beta using the singularities of the epsilon --> 0+ heteroclinic orbit in the complex plane. We then estimate gamma using linearization about orbits in the complex plane. These estimates, as well as the assertions regarding the behavior of the functions in the complex plane, are supported by our numerical calculations.