具有超指数闭柱面的自相似集
Self-similar sets with super-exponential close cylinders
摘要：
S. Baker（2019），B. Bárány和A. Käenmäki（2019）独立地证明了存在没有精确重叠的迭代函数系统，并且在所有小水平上都存在超指数闭合圆柱体。我们采用S.贝克，并获得更多的例子，这种类型。证明了对任意代数数$β\ge 2$，存在实数$s, t$使得迭代函数系$$ \left \{\frac{x}β, \frac{x+1}β, \frac{x+s}β, \frac{x+t}β\right \} $$满足上述性质.
英文摘要：
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.
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