Seminari del Dipartimento



Multiple expansions in non-integer bases

Vilmos Komornik

02-02-2022 - 16:00
Largo San Leonardo Murialdo,1 - Pal.C


We report on a joint work with Yuru Zou and Jian Lu on multiple expansions in non-integer bases.
Let $U_q^j$ denote the set of real numbers having exactly $j$ expansions in base $q$ over the two-digit alphabet $set{0,1}$.
We investigate the closedness of the sets $U_q^j$.
Next, motivated by an example of Sidorov, we exhibit many special bases in which the Hausdorff dimension of $U_q^j$ is the same for all finite $j$.

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