Critical bases for ternary alphabets

Abstract

Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant $q^{\prime }\approx 1.78723$ in non-integer base expansions on two-letter alphabets: in bases $1<q<q^{\prime }$ only countably numbers have unique expansions, while for $q\ge q^{\prime }$ there is a continuum of such numbers. We investigate the analogous question for ternary alphabets.

27 pages, 9 figures