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Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

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Period doubling cascades in high dimensional systems
by
Evelyn Sander
George Mason University

Period doubling cascades were first discovered in 1962, and have since been a hallmark in the study of dynamical behavior. Feigenbaum's famous results for rigorous demonstrations of cascades and the universality of their placement have been used for a large variety of one-dimensional maps which are similar to quadratic maps. Yorke and Alligood and Franks took a topological point of view for showing that a dynamical change in behavior of a map results as a parameter is varied results in period doubling cascades. We are able to extend these results and apply it to a much richer set of examples than previously done. In particular, we look at period doubling cascades for certain arbitrarily large coupled systems.

Date received: February 28, 2008

Copyright © 2008 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 # cawy-08.