%0 Journal Article
%T Generalized golden ratios of ternary alphabets
%A Vilmos Komornik
%A Anna Chiara Lai
%A Marco Pedicini
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0901.1114v1