American Institute of Mathematical Sciences

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2011, 2011(Special): 903-912. doi: 10.3934/proc.2011.2011.903

Minimality in iterative systems of Möbius transformations

Petr Kůrka 1,

1. 

Center for Theoretical Study, Academy of Sciences and Charles University in Prague, Jilská 1, CZ-11000 Praha 1

Received  July 2010 Revised  March 2011 Published  October 2011

We study the parameter space of an iterative system consisting of two hyperbolic disc Möbius transformations. We identify several classes of parameters which yield discrete groups whose fundamental polygons have sides at the Euclidean boundary. It follows that these system are not minimal.
Keywords: iterative Möbius systems, topological dynamics, minimal systems.
Mathematics Subject Classification: Primary: 54H20; Secondary: 37F30.
Citation: Petr Kůrka. Minimality in iterative systems of Möbius transformations. Conference Publications, 2011, 2011 (Special) : 903-912. doi: 10.3934/proc.2011.2011.903
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