On the Diophantine nature of the elements of Cantor sets arising in the dynamics of contracted rotations

DOI10.2422/2036-2145.202001_008zbMath1487.11073arXiv2001.00380OpenAlexW2997608277MaRDI QIDQ5037192

Arnaldo Nogueira, Dong Han Kim, Michel Laurent, Yann Bugeaud

Publication date: 28 February 2022

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.00380

zbMATH Keywords

Cantor setirrational numberalgebraic numberSturmian number

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Dynamical systems involving maps of the interval (37E05)

Related Items (2)

Combinatorial structure of Sturmian words and continued fraction expansion of Sturmian numbers ⋮ Dynamics of piecewise increasing contractions

Cites Work

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• Substitutions in dynamics, arithmetics and combinatorics
• Diophantine approximation
• Transcendence of numbers with a low complexity expansion
• Rotation number of contracted rotations
• Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series
• Neurons
• The number of subspaces occurring in the p-adic subspace theorem in diophantine approximation.
• Initial powers of Sturmian sequences
• Some suggestions for further research
• Calcul de la dynamique de transformations linéaires contractantes mod 1 et arbre de Farey
• A new complexity function, repetitions in Sturmian words, and irrationality exponents of Sturmian numbers
• A piecewise contractive dynamical system and Phragmèn's election method

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