Geodesic
Generalized golden ratios of ternary alphabets
Journal of the European Mathematical Society, Tome 13 (2011) no. 4, pp. 1113-1146.

Voir la notice de l'article provenant de la source EMS Press

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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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. http://geodesic.mathdoc.fr/articles/10.4171/jems/277/

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