Dynamics of Number Systems by Petr Kůrka

Author:Petr Kůrka
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The interval cylinders are obtained from the unique paths with source : , , . Thus and (F, G, V) is a sofic number system.

Consider the binary signed system with alphabet and forbidden words . The vertices of the deterministic labelled graph are prefixes of the forbidden words . The graph together with the V-intervals is in Fig. 4.10. We have

Thus and (F, G, V) is a sofic number system.

Fig. 4.10The deterministic graph of the binary signed system

Fig. 4.11Expansion of rational numbers in the system of signed continued fractions according to Definition 4.17 (top) and according to Definition 4.33 in the sofic number system with the graph from Fig. 4.9 (bottom)

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