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2005 Spring Topology and Dynamics Conference
March 17-19, 2005
Berry College
Mount Berry, Georgia, USA

Organizers
Eric McDowell, Todd Timberlake, John Graham

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Braids, index theory, and parabolic PDEs
by
Robert Ghrist
University of Illinois, Urbana-Champaign
Coauthors: R. Vandervorst

We use ideas from braid theory and Morse theory to give a topological version of the comparison principle for scalar parabolic PDEs. This allows us to prove a `Sharkovsky-like' forcing theory for PDEs based on braid classes. This is strongly reminiscent of Boyland's work on braid types for 2-d maps, but it applies to the (infinite dimensional) dynamics of PDEs.

Date received: February 28, 2005

Copyright © 2005 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 # capc-66.