Möbius iterated function systems

Vince, Andrew

doi:10.1090/S0002-9947-2012-05624-8

Möbius iterated function systems
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Trans. Amer. Math. Soc. 365 (2013), 491-509 Request permission

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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