Properties of Mobius number systems
Alexandr Kazda · arXiv (Cornell University) · 2009
Möbius number systems represent points using sequences of Möbius transformations. Thorough the paper, we are mainly interested in representing the unit circle (which is equivalent to representing R ∪ {∞}). The main aim of the paper is to improve already known tools for proving that a given subshift–iterative system pair is in fact a Möbius number system. We also study the existence problem: How to describe iterative systems resp. subshifts for which there exists a subshift resp. iterative system such that the resulting pair forms a Möbius number system. While we were unable to provide a complete answer to this question, we present both positive and negative partial results. As Möbius number systems are also subshifts, we can ask when a given Möbius number system is sofic. We give this problem a short treatment at the end of our paper.