Minimality in iterative systems of Möbius transformations

Petr Kůrka

doi:10.3934/proc.2011.2011.903

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2011, Volume 2011: 903-912. Doi: 10.3934/proc.2011.2011.903 open access

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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: June 30, 2010

Revised: February 28, 2011

Published: August 2017

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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.

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Mathematics Subject Classification: Primary: 54H20; Secondary: 37F30.

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