Hausdorff dimension of the multiplicative golden mean shift

Richard Kenyon; Yuval Peres; Boris Solomyak

Hausdorff dimension of the multiplicative golden mean shift

Dynamical Systems 2018-02-08 v2 Number Theory

Authors: Richard Kenyon , Yuval Peres , Boris Solomyak

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.

Keywords

hausdorff dimension multiplicative golden mean shift minkowski dimension binary expansion

Cite

@article{arxiv.1105.3441,
  title  = {Hausdorff dimension of the multiplicative golden mean shift},
  author = {Richard Kenyon and Yuval Peres and Boris Solomyak},
  journal= {arXiv preprint arXiv:1105.3441},
  year   = {2018}
}

Comments

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

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