B.O.Stratmann M.Kesseboehmer
A multifractal analysis for Stern-Brocot intervals]{A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates
Preprint series: Mathematica Gottingensis
MSC:
11J70 Continued fractions and generalizations, See also {11A55, 11K50}
11J83 Metric theory
Abstract: In this paper we obtain multifractal generalizations of classical
results by LÚvy 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.

Keywords: Multifractal analysis,number theory, metrical Diophantine analysis