The break-up of a heteroclinic connection in a volume preserving mapping

Abstract We consider a family of three-dimensional, volume preserving maps depending on a small parameter e. As e→0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for small e the heteroclinic connection breaks up and that the splitting between its components scales with e like eγ exp(-β/e). We estimate β using the singularities of the e→0+ heteroclinic orbit in the complex plane. We then estimate γ using linearization about orbits in the complex plane. While these estimates are not proven, they are well supported by our numerical calculations. The work described here is a special case of the theory derived by Amick et al. which applies to q-dimensional volume preserving mappings.