A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates
Number Theory
2007-06-20 v2 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.math/0509603,
title = {A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates},
author = {Marc Kesseböhmer and Bernd O. Stratmann},
journal= {arXiv preprint arXiv:math/0509603},
year = {2007}
}
Comments
25 pages, 4 figures