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

DOI10.1515/CRELLE.2007.029zbMath1117.37003arXivmath/0509603OpenAlexW2038701226MaRDI QIDQ3445259

Bernd O. Stratmann, Marc Kesseböhmer

Publication date: 8 June 2007

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509603

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Fractals (28A80) Diophantine approximation in probabilistic number theory (11K60)

Related Items (37)

Spectral theory of regular sequences ⋮ Dimension spectra of hyperbolic flows ⋮ On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps ⋮ Strong renewal theorems and Lyapunov spectra forα-Farey andα-Lüroth systems ⋮ Big Birkhoff sums in $d$-decaying Gauss like iterated function systems ⋮ The Lyapunov spectrum is not always concave ⋮ Minkowski's question mark measure ⋮ On the fast Khintchine spectrum in continued fractions ⋮ Billiards on Pythagorean triples and their Minkowski functions ⋮ On the derivative of the \(\alpha\)-Farey-Minkowski function ⋮ Lyapunov spectra for KMS states on Cuntz-Krieger algebras ⋮ Statistical distribution of the Stern sequence ⋮ Approximation orders of real numbers by \(\beta\)-expansions ⋮ SLOW GROWTH RATE OF THE DIGITS IN ENGEL EXPANSIONS ⋮ The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps ⋮ Infinite non-conformal iterated function systems ⋮ Beta-expansion and continued fraction expansion of real numbers ⋮ Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets ⋮ Large deviations for denominators of continued fractions ⋮ Birkhoff spectrum for piecewise monotone interval maps ⋮ Stability and perturbations of countable Markov maps ⋮ Precise asymptotics on the Birkhoff sums for dynamical systems ⋮ Derivatives of slippery Devil's staircases ⋮ Transience and multifractal analysis ⋮ Fractal analysis for sets of non-differentiability of Minkowski's question mark function ⋮ Dimension theory for multimodal maps ⋮ The arithmetic-geometric scaling spectrum for continued fractions ⋮ Multifractal analysis of the Lyapunov exponent for the backward continued fraction map ⋮ Large deviation principle for arithmetic functions in continued fraction expansion ⋮ Regularity of multifractal spectra of conformal iterated function systems ⋮ Regularity of Minkowski's question mark measure, its inverse and a class of IFS invariant measures ⋮ How many inflections are there in the Lyapunov spectrum? ⋮ Frequency of digits in the Lüroth expansion ⋮ The n-dimensional Stern–Brocot tree ⋮ Two arithmetic applications of perturbations of composition operators ⋮ Limit theorems for counting large continued fraction digits ⋮ Counting the Lyapunov inflections in piecewise linear systems*

Cites Work

• On the thermodynamic formalism for the Gauss map
• Group completions and limit sets of Kleinian groups
• Dimension theory and Fuchsian groups
• Thermodynamic formalism and multifractal analysis of conformal infinite iterated function systems
• Multifractal analysis of Lyapunov exponent for continued fraction and Manneville-Pomeau transformations and applications to diophantine approximation
• Large deviation for weak Gibbs measures and multifractal spectra
• Fractal measures and their singularities: The characterization of strange sets
• Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
• A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups
• Multifractal analysis of weak Gibbs measures and phase transition—application to some Bernoulli convolutions
• Multifractal formalism for some parabolic maps
• Thermodynamic formalism for countable Markov shifts
• [https://portal.mardi4nfdi.de/wiki/Publication:5612191 Une d�monstration simplifi�e et une extension de la formule d'Abramov sur l'entropie des transformations induites]
• STERN–BROCOT PRESSURE AND MULTIFRACTAL SPECTRA IN ERGODIC THEORY OF NUMBERS
• On the notion of recurrence in discrete stochastic processes
• Gibbs states on the symbolic space over an infinite alphabet

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