Dynamics forβ-shifts and Diophantine approximation

DOI10.1017/S0143385707000223zbMath1140.11035MaRDI QIDQ5436446

Boris Adamczewski, Yann Bugeaud

Publication date: 16 January 2008

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

transcendencediophantine approximation\(\beta\)-shiftPisot and Salem numberslinear forms with algebraic coefficients

Mathematics Subject Classification ID

Combinatorics on words (68R15) Transcendence (general theory) (11J81) Simultaneous homogeneous approximation, linear forms (11J13) Symbolic dynamics (37B10) Automata sequences (11B85)

Related Items (24)

The critical exponent functions ⋮ Continued fractions with low complexity: transcendence measures and quadratic approximation ⋮ The points with dense orbit under the \(\beta\)-expansions of different bases ⋮ On the expansion of some exponential periods in an integer base ⋮ Squares and cubes in Sturmian sequences ⋮ The digit exchanges in the rotational beta expansions of algebraic numbers ⋮ Quadratic approximation to automatic continued fractions ⋮ APPROXIMATION ORDERS OF A REAL NUMBER IN A FAMILY OF BETA-DYNAMICAL SYSTEMS ⋮ A note on non-periodic greedy expansions in Salem base ⋮ Approximation orders of real numbers by \(\beta\)-expansions ⋮ Initial nonrepetitive complexity of regular episturmian words and their Diophantine exponents ⋮ Beta-shifts, their languages, and computability ⋮ Beta-expansion and continued fraction expansion of real numbers ⋮ A devil's staircase from rotations and irrationality measures for Liouville numbers ⋮ A new complexity function, repetitions in Sturmian words, and irrationality exponents of Sturmian numbers ⋮ On the \(b\)-ary expansion of an algebraic number ⋮ Nombres self normaux ⋮ The Critical Exponent is Computable for Automatic Sequences ⋮ EXCEPTIONAL SETS RELATED TO THE RUN-LENGTH FUNCTION OF BETA-EXPANSIONS ⋮ On the computational complexity of algebraic numbers: the Hartmanis–Stearns problem revisited ⋮ APPROXIMATION PROPERTIES OF THE ORBITS UNDER β-TRANSFORMATION ⋮ Nombres réels de complexité sous-linéaire : mesures d'irrationalité et de transcendance ⋮ Binary words with a given Diophantine exponent ⋮ On the beta-expansions of 1 and algebraic numbers for a Salem number beta

Cites Work

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• Points génériques de Champernowne sur certains systèmes codes; application aux θ-shifts
• On Periodic Expansions of Pisot Numbers and Salem Numbers
• Symbolic dynamics for $\beta$-shifts and self-normal numbers
• On the Random Character of Fundamental Constant Expansions
• On the beta expansion for Salem numbers of degree 6

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