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

Yuval Peres; Joerg Schmeling; Stéphane Seuret; Boris Solomyak

doi:10.1007/s11856-013-0058-z

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

Yuval Peres, Joerg Schmeling, Stéphane Seuret, Boris Solomyak

Research output: Contribution to journal › Article › peer-review

Abstract

We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σ_m={0,..,m−1}^ℕ that are invariant under multiplication by integers. The results apply to the sets {x∈Σ_m:∀ k, x_kx_2k.. x_nk =0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.

Original language	English
Pages (from-to)	687-709
Number of pages	23
Journal	Israel Journal of Mathematics
Volume	199
Issue number	2
DOIs	https://doi.org/10.1007/s11856-013-0058-z
State	Published - 1 Mar 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/s11856-013-0058-z

Cite this

@article{fef66a4b45194c97a2e6a7cc7b8e02a6,

title = "Dimensions of some fractals defined via the semigroup generated by 2 and 3",

abstract = "We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σm={0,..,m−1}ℕ that are invariant under multiplication by integers. The results apply to the sets {x∈Σm:∀ k, xkx2k.. xnk =0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.",

author = "Yuval Peres and Joerg Schmeling and St{\'e}phane Seuret and Boris Solomyak",

note = "Publisher Copyright: {\textcopyright} 2014, Hebrew University Magnes Press.",

year = "2014",

month = mar,

day = "1",

doi = "10.1007/s11856-013-0058-z",

language = "الإنجليزيّة",

volume = "199",

pages = "687--709",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Dimensions of some fractals defined via the semigroup generated by 2 and 3

AU - Peres, Yuval

AU - Schmeling, Joerg

AU - Seuret, Stéphane

AU - Solomyak, Boris

PY - 2014/3/1

Y1 - 2014/3/1

N2 - We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σm={0,..,m−1}ℕ that are invariant under multiplication by integers. The results apply to the sets {x∈Σm:∀ k, xkx2k.. xnk =0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.

AB - We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σm={0,..,m−1}ℕ that are invariant under multiplication by integers. The results apply to the sets {x∈Σm:∀ k, xkx2k.. xnk =0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.

UR - http://www.scopus.com/inward/record.url?scp=84886901630&partnerID=8YFLogxK

U2 - 10.1007/s11856-013-0058-z

DO - 10.1007/s11856-013-0058-z

M3 - مقالة

SN - 0021-2172

VL - 199

SP - 687

EP - 709

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this