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Marc Kessebhmer, Bernd O Stratmann

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

In this paper we obtain multifractal generalizations of classical results by Lévy 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.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2007, 04/2007
Pages: 133 - 163

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