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

Peres, Yuval; Schmeling, Jörg LU ; Seuret, Stephane and Solomyak, Boris (2014) In Israel Journal of Mathematics 199(2). p.687-709
Abstract
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.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Israel Journal of Mathematics
volume
199
issue
2
pages
687 - 709
publisher
Hebrew University Magnes Press
external identifiers
  • wos:000338204300010
  • scopus:84886901630
ISSN
0021-2172
DOI
10.1007/s11856-013-0058-z
language
English
LU publication?
yes
id
bbc549d7-10e2-42e4-8957-8f2501b92697 (old id 4608733)
date added to LUP
2014-09-04 12:05:26
date last changed
2017-10-01 04:26:47
@article{bbc549d7-10e2-42e4-8957-8f2501b92697,
  abstract     = {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.},
  author       = {Peres, Yuval and Schmeling, Jörg and Seuret, Stephane and Solomyak, Boris},
  issn         = {0021-2172},
  language     = {eng},
  number       = {2},
  pages        = {687--709},
  publisher    = {Hebrew University Magnes Press},
  series       = {Israel Journal of Mathematics},
  title        = {Dimensions of some fractals defined via the semigroup generated by 2 and 3},
  url          = {http://dx.doi.org/10.1007/s11856-013-0058-z},
  volume       = {199},
  year         = {2014},
}