A devil's staircase from rotations and irrationality measures for Liouville numbers

DOI10.1017/S0305004108001606zbMath1204.37041arXiv0709.1642MaRDI QIDQ3542115

Do Yong Kwon

Publication date: 28 November 2008

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

Full work available at URL: https://arxiv.org/abs/0709.1642

Mathematics Subject Classification ID

Combinatorics on words (68R15) Dynamical systems involving maps of the circle (37E10) Measures of irrationality and of transcendence (11J82) Symbolic dynamics (37B10)

Related Items (8)

Newton representation of functions over natural integers having integral difference ratios ⋮ Unnamed Item ⋮ Moments of discrete measures with dense jumps induced by \(\beta\)-expansions ⋮ Digit frequencies of beta-expansions ⋮ A one-parameter family of Dirichlet series whose coefficients are Sturmian words ⋮ Exceptional parameters of linear mod one transformations and fractional parts \(\{ \xi (p/q)^n \}\) ⋮ Discontinuous, although ``highly differentiable, real functions and algebraic genericity ⋮ A two-dimensional singular function via Sturmian words in base \(\beta\)

Cites Work

• Unnamed Item
• Transcendence of numbers with a low complexity expansion
• Transcendence of Sturmian or morphic continued fractions
• \(\beta\)-expansions and symbolic dynamics
• Sturmian words, \(\beta\)-shifts, and transcendence
• On gaps in Rényi \(\beta\)-expansions of unity for \(\beta>1\) an algebraic number
• On the complexity of algebraic numbers. II: Continued fractions
• On theβ-expansions of real numbers
• Diophantine properties of real numbers generated by finite automata
• Dynamics forβ-shifts and Diophantine approximation

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