论文标题
中间三分之二的二元近似
Dyadic Approximation in the Middle-Third Cantor Set
论文作者
论文摘要
在本文中，我们研究了中间三分之一第托集中的二元近似的度量理论。该理论补充了Levesley，Salp和Velani（2007）的早期工作，后者研究了由三合会理性设定的cantor中的近似问题。我们发现，当我们考虑Cantor集合中的二元近似时的行为与考虑在Cantor集合中的三合会近似大不相同。从某种意义上说，这种行为的差异是弗斯滕贝格的时间2倍3倍的3倍来自动力学系统的现象，这表明基本2和基本3的扩展不是一个结构化的。
In this paper, we study the metric theory of dyadic approximation in the middle-third Cantor set. This theory complements earlier work of Levesley, Salp, and Velani (2007), who investigated the problem of approximation in the Cantor set by triadic rationals. We find that the behaviour when we consider dyadic approximation in the Cantor set is substantially different to considering triadic approximation in the Cantor set. In some sense, this difference in behaviour is a manifestation of Furstenberg's times 2 times 3 phenomenon from dynamical systems, which asserts that the base 2 and base 3 expansions of a number are not both structured.
