Geodesic
Generalized golden ratios of ternary alphabets
Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 1113-1146
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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.
DOI : 10.4171/jems/277
Classification : 11-XX, 00-XX
Keywords: Golden ratio, ternary alphabet, unique expansion, noninteger base, beta-expansion, greedy expansion, lazy expansion, univoque sequence 
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     title = {Generalized golden ratios of ternary alphabets},
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Vilmos Komornik; Anna Chiara Lai; Marco Pedicini. Generalized golden ratios of ternary alphabets. Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 1113-1146. doi: 10.4171/jems/277

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