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

M Kesseboehmer; Bernd O Stratmann

doi:10.1515/CRELLE.2007.029

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

M Kesseboehmer, Bernd O Stratmann

Pure Mathematics

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

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 language	English
Pages (from-to)	133-163
Number of pages	31
Journal	Journal fuer die Reine und Angewandte Mathematik
Volume	2007
Issue number	605
DOIs	https://doi.org/10.1515/CRELLE.2007.029
Publication status	Published - Apr 2007

Keywords

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

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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.",

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AB - 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.

KW - WEAK GIBBS MEASURES

KW - THERMODYNAMIC FORMALISM

KW - KLEINIAN-GROUPS

KW - TRANSFORMATIONS

KW - DIMENSION

KW - ENTROPY

KW - SETS

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DO - 10.1515/CRELLE.2007.029

M3 - Article

VL - 2007

SP - 133

EP - 163

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

IS - 605

ER -

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

Abstract

Keywords

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