Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension approximation of attractors of graph directed IFSs by
  self-similar sets   We show that for the attractor $(K_{1},\dots,K_{q})$ of a graph directed
iterated function system, for each $1\leq j\leq q$ and $\varepsilon>0$ there
exits a self-similar set $K\subseteq K_{j}$ that satisfies the strong
separation condition and $\dim_{H}K_{j}-\varepsilon<\dim_{H}K$. We show that we
can further assume convenient conditions on the orthogonal parts and similarity
ratios of the defining similarities of $K$. Using this property as a `black
box' we obtain results on a range of topics including on dimensions of
projections, intersections, distance sets and sums and products of sets.

6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci