Beyond All Orders: Singular Perturbations in a Mapping
نویسنده
چکیده
We consider a family of q-dimensional (q > 1), volume-preserving maps depending on a small parameter ~. As e ---> 0 + these maps asymptote to flows which attain a heteroclinic connection. We show that for small ~ the heteroclinic connection breaks up and that the splitting between its components scales with e like ~ r exp [ / 3 / e ] . We estimate /3 using the singularities of the B ---> 0 ÷ heteroclinic orbit in the complex plane. We then estimate 3' 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.
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