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

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dc.creatorKesseböhmer, Marc
dc.creatorStratmann, Bernd O.
dc.date2005-09-26
dc.date2005-12-09
dc.date.accessioned2026-07-07T08:11:11Z
dc.date.available2026-07-07T08:11:11Z
dc.descriptionIn 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.
dc.description25 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0509603
dc.identifierhttp://arxiv.org/abs/math/0509603
dc.identifierJournal fuer die reine und angewandte Mathematik (Crelle's Journal) 605 (2007), 133-163
dc.identifierdoi:10.1515/CRELLE.2007.029
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132045
dc.subjectNumber Theory
dc.subjectDynamical Systems
dc.subject37A45; 11J70; 11J83; 28A80
dc.titleA multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates
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