Infinite Ergodic Theory of Numbers

DOI10.1515/9783110439427zbMath1362.37003OpenAlexW2530771303MaRDI QIDQ2797267

Bernd O. Stratmann, Sara Munday, Marc Kesseböhmer

Publication date: 5 April 2016

Full work available at URL: https://doi.org/10.1515/9783110439427

zbMATH Keywords

dynamical systemscontinued fractionsinfinite ergodic theoryGauss measureFarey mapquestion mark function

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Continued fractions and generalizations (11J70) Metric theory of continued fractions (11K50) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

Related Items (15)

On Minkowski type question mark functions associated with even or odd continued fractions ⋮ Statistical distribution of the Stern sequence ⋮ On special representations of automorphisms of \(\sigma\)-finite measure spaces using Poincaré recurrence theorem and Hopf decomposition ⋮ Diophantine approximation by negative continued fraction ⋮ A slow triangle map with a segment of indifferent fixed points and a complete tree of rational pairs ⋮ Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails ⋮ Intermediately trimmed strong laws for Birkhoff sums on subshifts of finite type ⋮ Strong laws of large numbers for intermediately trimmed Birkhoff sums of observables with infinite mean ⋮ Infinite mixing for one-dimensional maps with an indifferent fixed point ⋮ Introducing Minkowski normality ⋮ Two arithmetic applications of perturbations of composition operators ⋮ Limit theorems for counting large continued fraction digits ⋮ Distribution of periodic points of certain Gauss shifts with infinite invariant measure ⋮ Distribution of the reduced quadratic irrationals arising from the odd continued fraction expansion ⋮ Representation and coding of rational pairs on a triangular tree and Diophantine approximation in $\mathbb R^2$

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