论文标题
自相似的套件，带有超指数的闭合缸
Self-similar sets with super-exponential close cylinders
论文作者
论文摘要
S. Baker（2019），B.Bárány和A.Käenmäki（2019）独立地表明，迭代功能系统没有确切的重叠，并且在所有小级别上都有超过指数的近距离圆柱。我们适应了S. baker的方法，并获得了这种类型的进一步示例。 We prove that for any algebraic number $β\ge 2$ there exist real numbers $s, t$ such that the iterated function system $$ \left \{\frac{x}β, \frac{x+1}β, \frac{x+s}β, \frac{x+t}β\right \} $$ satisfies the above property.
S. Baker (2019), B. Bárány and A. Käenmäki (2019) independently showed that there exist iterated function systems without exact overlaps and there are super-exponentially close cylinders at all small levels. We adapt the method of S. Baker and obtain further examples of this type. We prove that for any algebraic number $β\ge 2$ there exist real numbers $s, t$ such that the iterated function system $$ \left \{\frac{x}β, \frac{x+1}β, \frac{x+s}β, \frac{x+t}β\right \} $$ satisfies the above property.
