%0 Journal Article
%T Hausdorff dimension for fractals invariant under the multiplicative integers
%A Richard Kenyon
%A Yuval Peres
%A Boris Solomyak
%J Mathematics
%D 2011
%I arXiv
%X We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences $(x_k)$ such that $x_k x_{2k}=0$ for all $k$. We compute the Hausdorff and Minkowski dimensions of these sets and show that they are typically different. The proof proceeds via a variational principle for multiplicative subshifts.
%U http://arxiv.org/abs/1102.5136v2