Properties of Moebius number systems

Kazda, Alexandr
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Moebius number systems represent points using sequences of Moebius transformations. Thorough the paper, we are mainly interested in representing the unit circle (which is equivalent to representing R\cup\{\infty\}). 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 Moebius 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 Moebius number system. While we were unable to provide a complete answer to this question, we present both positive and negative partial results. As Moebius number systems are also subshifts, we can ask when a given Moebius number system is sofic. We give this problem a short treatment at the end of our paper.
Comment: 50 pages, 13 figures
Mathematics - Dynamical Systems, Mathematics - Number Theory, 40A05, 11K99, 37B10