Continuation from the Anti-Integrable limit: Symbolic Dynamics and Bifurcations
by
James Meiss
University of Colorado at Boulder
Coauthors: David Sterling

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. Using the Hénon map as an example, we obtain a simple analytical bound on the domain of existence of the horseshoe that is equivalent to the well-known bound of Devaney and Nitekei. We also reformulate the popular method for finding periodic orbits introduced by Biham and Wenzel. Near an anti-integrable limit, we show that this method is guaranteed to converge. This formulation puts the choice of symbolic dynamics, required for the algorithm, on a firm foundation.

Date received: February 19, 1998

Copyright © 1998 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 Mathematical Conference Abstracts. Document # cabf-02.