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Dimensions of some fractals defined via the semigroup generated by 2 and 3

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Author

Summary, in English

We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Sigma(m) ={0, ... , m-1}(N) that are invariant under multiplication by integers. The results apply to the sets {x is an element of Sigma(m): for all k, x(k)x(2k) ... x(nk) = 0}, where n >= 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.

Department/s

Publishing year

2014

Language

English

Pages

687-709

Publication/Series

Israel Journal of Mathematics

Volume

199

Issue

2

Document type

Journal article

Publisher

Hebrew University Magnes Press

Topic

  • Mathematics

Status

Published

Research group

  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 0021-2172