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Pré-Publication, Document De Travail Année : 2020

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

Dong Han Kim
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  • PersonId : 968721
Arnaldo Nogueira
  • Fonction : Auteur
  • PersonId : 829877

Résumé

We prove that these Cantor sets are made up of transcendental numbers, apart from their endpoints $0$ and $1$, under some arithmetical assumptions on the data. To that purpose, we establish a criterion of linear independence over the field of algebraic numbers for the three numbers $1$, a characteristic Sturmian number, and an arbitrary Sturmian number with the same slope.

Dates et versions

hal-02451476 , version 1 (23-01-2020)

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Yann Bugeaud, Dong Han Kim, Michel Laurent, Arnaldo Nogueira. On the Diophantine nature of the elements of Cantor sets arising in the dynamics of contracted rotations. 2020. ⟨hal-02451476⟩
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