The Multiplicative golden mean shift has infinite Hausdorff measure

Details The Multiplicative golden mean shift has infinite Hausdorff measure The Multiplicative golden mean shift has infinite Hausdorff measure

2012-01-27

arxiv.org/abs/1201.5842v2

Mathematics

Dynamical Systems

18 pages; minor revision after the referee report; to appear in Proceedings of the Conference on Fractals and Related Fields I

Scientific paper

In an earlier work, joint with R. Kenyon, we computed 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=1,2... Here we show that this set has infinite Hausdorff measure in its dimension. A more precise result in terms of gauges in which the Hausdorff measure is infinite is also obtained.

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