Unique infinite expansions in noninteger bases

Author： Komornik Vilmos  

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.134, Iss.3, 2012-02, pp. : 344-355

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Abstract

Contrary to the classical situation, in noninteger bases almost all numbers have a continuum of distinct expansions. However, the set of numbers having a unique expansions also has a rich topological and combinatorial structure. We clarify the connection of this set with the sets of numbers having a unique infinite or doubly infinite expansion.

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