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21st Summer Conference on Topology and its Applications
July 6-9, 2006
Georgia Southern University
Statesboro, GA, USA

Organizers
Martha Abell, Francis Jordan, Frédéric Mynard, Sze-Man Ngai

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Sierpinski Curves Galore
by
Robert L. Devaney
Boston University

In this talk we discuss the dynamical behavior of the family of complex rational maps of the form zn + C / zd where n > 1 and C is a complex parameter. We shall show that there are many different parameters for which the Julia set of such a map is a Sierpinski curve, i.e., homeomorphic to the Sierpinski carpet fractal. Therefore all of these sets are homeomorphic to one another. However, we will show that there are many very different ways that this structure can arise and that therefore the corresponding maps are dynamically distinct (not topologically conjugate) on these different sets.

Date received: May 11, 2006

Copyright © 2006 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 # carh-18.