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arXiv · 2001.00380

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

Yann Bugeaud·Dong Han Kim·Michel Laurent·Arnaldo Nogueira
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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.

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Yann Bugeaud, Dong Han Kim, Michel Laurent, Arnaldo Nogueira. 2020-01-02. On the Diophantine nature of the elements of Cantor sets arising in the dynamics of contracted rotations. https://arxiv.org/abs/2001.00380

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