论文标题
关于旋转动力学的cantor集元素的寄生性质
On the Diophantine nature of the elements of Cantor sets arising in the dynamics of contracted rotations
论文作者
论文摘要
我们证明，在数据上的某些算术假设下，这些cantor套件由先验数字组成，除了它们的端点$ 0 $和$ 1 $。为此，我们在三个数字$ 1 $的代数数字上建立了线性独立的标准，一个特征性的sturmian数字以及一个具有相同斜率的sturmian号码。
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.
