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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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Essential balanced pairs and the Rauzy Fractal
by
Adrian Soto
Montana State University

Given a Pisot substitution, we give a characterization of connectedness of their associated Rauzy Fractal in terms of the essential balanced pairs of the substitution. Next, we show that when two tiling spaces are homeomorphic, via a rewriting, then we can decompose one of the associated fractals, rearrange the pieces and then obtain the second associated fractal. As a result, we provide an example of a connected Rauzy Fractal, with a rewriting having a non connected Rauzy Fractal. We also adapt a proof of Durand that will give us some restriction on the eigenvalues of the associated substitution.

Date received: February 11, 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 # cawk-41.