A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates

M Kesseboehmer, Bernd O Stratmann

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)

Abstract

In this paper we obtain multifractal generalizations of classical results by Levy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We give a complete multifractal analysis for Stern-Brocot intervals, for continued fractions and for certain Diophantine growth rates. In particular, we give detailed discussions of two multifractal. spectra closely related to the Farey map and to the Gauss map.

Original languageEnglish
Pages (from-to)133-163
Number of pages31
JournalJournal fuer die Reine und Angewandte Mathematik
Volume2007
Issue number605
DOIs
Publication statusPublished - Apr 2007

Keywords

  • WEAK GIBBS MEASURES
  • THERMODYNAMIC FORMALISM
  • KLEINIAN-GROUPS
  • TRANSFORMATIONS
  • DIMENSION
  • ENTROPY
  • SETS

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