Distribution of frequencies of digits via multifractal analysis

L Barreira, B Saussol, Jörg Schmeling

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskriftPeer review

Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)410-438
TidskriftJournal of Number Theory
Volym97
Nummer2
DOI
StatusPublished - 2002

Ämnesklassifikation (UKÄ)

  • Matematik

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