Convergence in Möbius Number Systems

Abstract

AbstractThe Möbius number systems use sequences of Möbius transformations to represent the extended real line or, equivalently, the unit complex circle. An infinite sequence of Möbius transformations represents a pointMoreover, we show how to improve a known result that guarantees the existence of Möbius number systems for some Möbius iterative systems.As Möbius number systems use subshifts instead of the whole symbolic space, we can ask what is the language complexity of these subshifts. We offer (under some assumptions) a sufficient and necessary condition for a number system to be sofic.