Generalized golden ratios of ternary alphabets

Details Generalized golden ratios of ternary alphabets Generalized golden ratios of ternary alphabets

2009-01-08

arxiv.org/abs/0901.1114v1

Mathematics

Number Theory

28 pages

Scientific paper

Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in function of the alphabets.

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