Critical bases for ternary alphabets

Abstract

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