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arXiv · 1105.3441

Hausdorff dimension of the multiplicative golden mean shift

Richard Kenyon·Yuval Peres·Boris Solomyak
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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.

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Richard Kenyon, Yuval Peres, Boris Solomyak. 2011-05-17. Hausdorff dimension of the multiplicative golden mean shift. https://arxiv.org/abs/1105.3441

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