论文标题
$δ$ - 换序列和飞机上的自相似集
$Δ$-revolving sequences and self-similar sets in the plane
论文作者
论文摘要
卡瓦穆拉（Kawamura）和艾伦（Allen）于1987年由Mizutani和ITO的作品发起，最近表明，某些由两个相似收缩概括的自相似集合具有自然的复杂功率序列表示，这是由过去依赖的旋转序列参数化的。 在本文中，我们概括了川村和艾伦的工作，以包括更广泛的自相似集合。我们表明，某些由两个以上相似收缩组成的自相似集也具有天然的复杂功率序列表示形式，该表示由{\ it $δ$ - 固定序列}参数化。该结果适用于其他几个著名的自相似套装，例如Heighway Dragon，Twindragon和Fudgeflake。
Initiated by Mizutani and Ito's work in 1987, Kawamura and Allen recently showed that certain self-similar sets generalized by two similar contractions have a natural complex power series representation, which is parametrized by past-dependent revolving sequences. In this paper, we generalize the work of Kawamura and Allen to include a wider collection of self-similar sets. We show that certain self-similar sets consisting of more than two similar contractions also have a natural complex power series representation, which is parametrized by {\it $Δ$-revolving sequences}. This result applies to several other famous self-similar sets such as the Heighway dragon, Twindragon, and Fudgeflake.
