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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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Classification of expansive attractors on surfaces
by
Brian Martensen
Minnesota State University
Coauthors: Marcy Barge

We prove the following conjecture of Hertz and Hertz: All transitive expansive attractors (of surfaces) are conjugate to either a hyperbolic attractor or a derived from pseudo-Anosov attractor.

Lewowicz and Hiraide established this result in the case in which the attractor is the entire manifold. Here we use the theory of prime ends to construct a new surface for the attractor. We are then able to extend the expansive dynamics to this entire surface to establish the result.

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-18.