Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a kind of self-similar sets with complete overlaps   Let $E$ be the self-similar set generated by the {\it iterated function
system} {\[ f_0(x)=\frac{x}{\beta},\quad f_1(x)=\frac{x+1}{\beta}, \quad
f_{\beta+1}=\frac{x+\beta+1}{\beta} \]}with $\beta\ge 3$. {Then} $E$ is a
self-similar set with complete {overlaps}, i.e., $f_{0}\circ
f_{\beta+1}=f_{1}\circ f_1$, 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.

8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con