Hausdorff dimension of the multiplicative golden mean shift

Abstract

We compute the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in $[0,1]$ whose binary expansion $(x_k)$ satisfies $x_k x_{2k}=0$ for all $k\ge 1$, and show that it is smaller than the Minkowski dimension.

5 pages, to appear in Comptes Rendus Mathematique; minor errors corrected