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

Marc Kesseböhmer·Bernd O. Stratmann
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Abstract

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 the Gauss map.

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Marc Kesseböhmer, Bernd O. Stratmann. 2005-12-09. A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates. https://doi.org/10.1515/crelle.2007.029

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