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- Title
Hausdorff dimension for fractals invariant under multiplicative integers.
- Authors
KENYON, RICHARD; PERES, YUVAL; SOLOMYAK, BORIS
- Abstract
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 (xk) such that xkx2k=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.
- Subjects
HAUSDORFF measures; DIMENSION theory (Algebra); FRACTALS; INVARIANTS (Mathematics); MATHEMATICAL sequences; ALGEBRAIC spaces; PROOF theory; VARIATIONAL principles
- Publication
Ergodic Theory & Dynamical Systems, 2012, Vol 32, Issue 5, p1567
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/S0143385711000538