The Multiplicative golden mean shift has infinite Hausdorff measure
Dynamical Systems
2012-04-19 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1201.5842,
title = {The Multiplicative golden mean shift has infinite Hausdorff measure},
author = {Yuval Peres and Boris Solomyak},
journal= {arXiv preprint arXiv:1201.5842},
year = {2012}
}
Comments
18 pages; minor revision after the referee report; to appear in Proceedings of the Conference on Fractals and Related Fields II (Porquerolles, June 2011)