Generalized golden ratios of ternary alphabets

  • Vilmos Komornik

    Université de Strasbourg, Strasbourg, France
  • Anna Chiara Lai

    Università di Roma La Sapienza, Italy
  • Marco Pedicini

    CNR, Roma, Italy


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.

Cite this article

Vilmos Komornik, Anna Chiara Lai, Marco Pedicini, Generalized golden ratios of ternary alphabets. J. Eur. Math. Soc. 13 (2011), no. 4, pp. 1113–1146

DOI 10.4171/JEMS/277