Beyond all orders: Singular perturbations in a mapping

摘要

We consider a family ofq-dimensional (q>1), volume-preserving maps depending on a small parameterε. Asε→ 0+these maps asymptote to flows which attain a heteroclinic connection. We show that for smallεthe heteroclinic connection breaks up and that the splitting between its components scales withεlikeεγexp-β/ε. We estimateβusing the singularities of theε→ 0+heteroclinic orbit in the complex plane. We then estimateγusing 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 numerica