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Distribution of frequencies of digits via multifractal analysis

Barreira, L; Saussol, B and Schmeling, Jörg LU (2002) In Journal of Number Theory 97(2). p.410-438
Abstract
We study the Hausdorff dimension of a large class of sets in the real line defined in terms of the distribution of frequencies of digits for the representation in some integer base. In particular, our results unify and extend classical work of Borel, Besicovitch, Eggleston, and Billingsley in several directions. Our methods are based on recent results concerning the multifractal analysis of dynamical systems and often allow us to obtain explicit expressions for the Hausdorff dimension. This work is still another illustration of the role that the theory of dynamical systems can play in number theory.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
multifractal analysis, frequencies of digits, Hausdorff dimension
in
Journal of Number Theory
volume
97
issue
2
pages
410 - 438
publisher
Academic Press
external identifiers
  • wos:000179838700013
  • scopus:0036907811
ISSN
0022-314X
DOI
10.1016/S0022-314X(02)00003-3
language
English
LU publication?
yes
id
1c49bb02-6aed-4d71-83e1-e188d6ecf3a6 (old id 321606)
date added to LUP
2007-08-08 09:20:43
date last changed
2017-06-25 04:31:01
@article{1c49bb02-6aed-4d71-83e1-e188d6ecf3a6,
  abstract     = {We study the Hausdorff dimension of a large class of sets in the real line defined in terms of the distribution of frequencies of digits for the representation in some integer base. In particular, our results unify and extend classical work of Borel, Besicovitch, Eggleston, and Billingsley in several directions. Our methods are based on recent results concerning the multifractal analysis of dynamical systems and often allow us to obtain explicit expressions for the Hausdorff dimension. This work is still another illustration of the role that the theory of dynamical systems can play in number theory.},
  author       = {Barreira, L and Saussol, B and Schmeling, Jörg},
  issn         = {0022-314X},
  keyword      = {multifractal analysis,frequencies of digits,Hausdorff dimension},
  language     = {eng},
  number       = {2},
  pages        = {410--438},
  publisher    = {Academic Press},
  series       = {Journal of Number Theory},
  title        = {Distribution of frequencies of digits via multifractal analysis},
  url          = {http://dx.doi.org/10.1016/S0022-314X(02)00003-3},
  volume       = {97},
  year         = {2002},
}