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, up to 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; ∈1; ∈2, where ∈1 and ∈2 are two arbitrary Sturmian numbers with the same slope.

Original languageEnglish
Pages (from-to)1691-1704
Number of pages14
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume22
Issue number4
DOIs
StatePublished - 2021

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