Abstract

In 1957 Renyi extended the familiar integer base expansions to non-integer bases. Erdős, Horvath and Joo started around 1990 to investigate the structure of all, not necessarily greedy expansions. We present some results in this field, obtained mostly in collaboration with Erdős, Joo, Loreti, Pethő, de Vries and Akiyama. For simplicity of exposition we consider only expansions in bases 1 < q ≤ 2, using the two-digit alphabet {0,1}. V. Komornik (University of Strasbourg) Expansions in non-integer bases Budapest, July 5, 2013 2 / 26

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