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Transactions of the American Mathematical Society

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Möbius iterated function systems

Author: Andrew Vince
Journal: Trans. Amer. Math. Soc. 365 (2013), 491-509
MSC (2010): Primary 28A80
Published electronically: August 7, 2012
MathSciNet review: 2984065
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Abstract: Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Möbius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, in terms of topological, geometric, and dynamical properties, of Möbius iterated function systems that possess an attractor. The paper also includes results on the duality between the attractor and repeller of a Möbius iterated function system.

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Andrew Vince
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611

Keywords: Iterated function systems, Möbius transformation
Received by editor(s): April 8, 2011
Received by editor(s) in revised form: May 9, 2011
Published electronically: August 7, 2012
Additional Notes: Thanks go to Michael Barnsley for always stimulating conversations on iterated function systems, and for graciously hosting my visit to the Australian National University, where much of this paper was written.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.