Minimality in iterative systems of Möbius transformations

Pages: 903 - 912, Issue Special, September 2011

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Petr Kůrka - Center for Theoretical Study, Academy of Sciences and Charles University in Prague, Jilská 1, CZ-11000 Praha 1, Czech Republic (email)

Abstract: 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:  topological dynamics, minimal systems, iterative Möbius systems
Mathematics Subject Classification:  Primary: 54H20; Secondary: 37F30

Received: July 2010;      Revised: March 2011;      Published: October 2011.