On the frequency of partial quotients of regular continued fractions

DOI10.1017/S0305004109990235zbMath1205.11090arXiv0906.3283MaRDI QIDQ3400950

Lingmin Liao, Ai-Hua Fan, Ji-Hua Ma

Publication date: 28 January 2010

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.3283

zbMATH Keywords

Hausdorff dimensionContinued fractionsfrequency of partial quotients

Mathematics Subject Classification ID

Metric theory of continued fractions (11K50)

Related Items (15)

Multifractal analysis for Markov interval maps with countably many branches ⋮ On new fractal phenomena connected with infinite linear IFS ⋮ Multifractal analysis on the level sets described by moving averages ⋮ A NONCONVENTIONAL STRONG LAW OF LARGE NUMBERS AND FRACTAL DIMENSIONS OF SOME MULTIPLE RECURRENCE SETS ⋮ On the fast Khintchine spectrum in continued fractions ⋮ Infinite non-conformal iterated function systems ⋮ Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets ⋮ Multifractal analysis of weighted ergodic averages ⋮ Multifractal analysis of Birkhoff averages for countable Markov maps ⋮ Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches ⋮ Maximizing Bernoulli measures and dimension gaps for countable branched systems ⋮ Multifractal analysis for expanding interval maps with infinitely many branches ⋮ On the Billingsley dimension of Birkhoff average in the countable symbolic space ⋮ Generic points of shift-invariant measures in the countable symbolic space ⋮ ON POINTS WITH POSITIVE DENSITY OF THE DIGIT SEQUENCE IN INFINITE ITERATED FUNCTION SYSTEMS

Cites Work

• Unnamed Item
• Billingsley dimension in probability spaces
• A remark on the growth of the denominators of convergents
• Dimension of some non-normal continued fraction sets
• Hausdorff dimension of some continued-fraction sets
• Fractal Dimensions and Random Transformations
• The dimension of some sets defined in terms of f-expansions
• A dimension gap for continued fractions with independent digits

This page was built for publication: On the frequency of partial quotients of regular continued fractions