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

Abstract : 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02451476
Contributor : Aigle I2m <>
Submitted on : Thursday, January 23, 2020 - 12:02:50 PM
Last modification on : Thursday, February 6, 2020 - 9:48:01 AM

Identifiers

• HAL Id : hal-02451476, version 1
• ARXIV : 2001.00380

Citation

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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