Splitting of separatrices and exponentially smallphenomena
by
Alexander Tovbis
University of Central Florida

We focus on further development of exponential asymptotic approach, introduced by Kruskal-Segur to study exponentially small splitting of homoclinic (heteroclinic) trajectories in singularly perturbed systems. In essence, this approach reduces the original problem to analysis of the Stokes phenomenon of a certain ``leading order" parameterless equation, associated with the system. We demonstrate on several examples (of singularly perturbed and discretized systems) how to make the connection between this ``leading order" equation and the full equation (so-called inner equation) rigorous. We also show how to extract ``more information" from the ``leading order" equation to approximate the ``split" trajectories. Remarkably, the same technique seems to work for for periodic solutions of the original unperturbed system.

Date received: February 14, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caep-02.