关于某些只含无理数的分形集

摘要：

本文证明了许多由相关的动力系统生成的分形集只包含无理数。作为应用，我们显式地构造了一些仅由无理数组成的重叠自相似集。

英文摘要：

In this paper, we prove that many fractal sets generated by the associated dynamical systems only contain irrationals. As an application, we explicitly construct some overlapping self-similar sets which only consist of irrationals.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。