Hausdorff dimension for fractals invariant under multiplicative integers

Richard Kenyon, Yuval Peres, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.

Original languageEnglish
Pages (from-to)1567-1584
Number of pages18
JournalErgodic Theory and Dynamical Systems
Issue number5
StatePublished - Oct 2012
Externally publishedYes


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