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Thurston Laminations which are invariant under the Map s3:S1→ S1
by
Jeffrey Houghton
University of Alabama at Birmingham
Abstract. W. Thurston used laminations of the unit disk (a special collection of disjoint chords called leaves) as a model for quadradic Julia sets and the Mandelbrot set. One fundamental result in the study of quadradic laminations is known as the Central Strip Lemma. This lemma provides a strong bound on the behaviour of the leaves under iteration of the map s2:S1→S1 defined by s2(t) = 2t mod 1. We will generalize this lemma to cubic laminations under the map s3(t) = 3t mod 1 and discuss applications of this generalization to cubic laminations and the resulting constraints upon cubic Julia sets.
Date received: February 20, 2009
Copyright © 2009 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 # cayo-16.