Critical bases for ternary alphabets

Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant $q'\approx1.78723$ in non-integer base expansions on two-letter alphabets: in bases $1<q<q'$ only countably numbers have unique expansions, while for $q\ge q'$ there is a continuum of such numbers. We investigate the analogous question for ternary alphabets.

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