论文标题
在一种自相似的集合上，有完整的重叠
On a kind of self-similar sets with complete overlaps
论文作者
论文摘要
令$ e $为由{\ it Iterated功能系统} {\ [f_0（x）= \ frac {x}β，\ quad f_1（x）= \ frac {x+1}β，\ quad F_ {β+1} = \ frac = \ frac = \ frac { $β\ ge 3 $。 {then} $ e $是一个自相似的集合，具有完整的{重叠}，即$ f_ {0} \ circ f_ {β+1} = f_ {1} \ circ f_1 $，但$ e $并非完全自相模仿。 我们研究了其所有生成的迭代功能系统，提供$ e $的频谱，并确定$ e $的Hausdorff Dimension和Hausdorff度量，以及包含有限或无限的不同三级代码的$ E $中所有点的集合。
Let $E$ be the self-similar set generated by the {\it iterated function system} {\[ f_0(x)=\frac{x}β,\quad f_1(x)=\frac{x+1}β, \quad f_{β+1}=\frac{x+β+1}β \]}with $β\ge 3$. {Then} $E$ is a self-similar set with complete {overlaps}, i.e., $f_{0}\circ f_{β+1}=f_{1}\circ f_1$, but $E$ is not totally self-similar. We investigate all its generating iterated function systems, give the spectrum of $E$, and determine the Hausdorff dimension and Hausdorff measure of $E$ and of the sets which contain all points in $E$ having finite or infinite different triadic codings.
