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