Dimensions of some fractals defined via the semigroup generated by 2 and 3
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4608733
- author
- Peres, Yuval ; Schmeling, Jörg LU ; Seuret, Stephane and Solomyak, Boris
- organization
- publishing date
- 2014
- 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
- 2016-04-01 14:41:23
- date last changed
- 2022-03-06 20:41:01
@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}},
doi = {{10.1007/s11856-013-0058-z}},
volume = {{199}},
year = {{2014}},
}