Hausdorff dimension of the multiplicative golden mean shift

Details Hausdorff dimension of the multiplicative golden mean shift Hausdorff dimension of the multiplicative golden mean shift

2011-05-17

arxiv.org/abs/1105.3441v2

Mathematics

Dynamical Systems

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

Scientific paper

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.

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