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
N1 - Publisher Copyright:
© 2014, Hebrew University Magnes Press.
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 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84886901630
SN - 0021-2172
VL - 199
SP - 687
EP - 709
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -