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

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

2005-09-26

arxiv.org/abs/math/0509603v2

Journal fuer die reine und angewandte Mathematik (Crelle's Journal) 605 (2007), 133-163

Mathematics

Number Theory

25 pages, 4 figures

Scientific paper

10.1515/CRELLE.2007.029

In this paper we obtain multifractal generalizations of classical results by L\'evy 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 the Gauss map.

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