A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates
By Marc Kessebohmer, Bernd Stratmann. 2005
104 citations recorded by the source corpus.
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 to the Gauss map.
Subfields: Economics and Econometrics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2d0e93b1b9fb98377e00eae3e547362abe5c6fa1
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Citations in the corpus
- Strong renewal theorems and Lyapunov spectra for α-Farey and α-Lüroth systems (2010, methodology): “Note that the Lyapunov spectra for the Gauss map and the Farey map have been determined in [16].”
- Fractal analysis for sets of non-differentiability of Minkowski's question mark function (2007, methodology): “In this disguise, the homeomorphismQ represents the topological conjugacy map between the Fareysystem and the tent system, such thatT ◦Q= Q◦F .”