Möbius number systems based on interval covers
Petr Kůrka, Alexandr Kazda · Nonlinearity · 2010
Given a finite alphabet A , a system of real orientation-preserving Möbius transformations , a subshift and an interval cover of , we consider the expansion subshift of all expansions of real numbers with respect to . If the expansion quotient is greater than 1 then there exists a continuous and surjective symbolic mapping and we say that is a Möbius number system. We apply our theory to the system of binary continued fractions which is a combination of the binary signed system with the continued fractions, and to the binary square system whose transformations have stable fixed points −1, 0, 1 and ∞.