Hausdorff dimension of the multiplicative golden mean shift

Preprint English OPEN
Kenyon, Richard; Peres, Yuval; Solomyak, Boris;
(2011)
  • Subject: 37C45 (Primary), 28A78, 37D35 (Secondary) | Mathematics - Dynamical Systems | Mathematics - Number Theory

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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