Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connectedness of fractals associated with Arnoux-Rauzy substitutions   Rauzy fractals are compact sets with fractal boundary that can be associated
with any unimodular Pisot irreducible substitution. These fractals can be
defined as the Hausdorff limit of a sequence of compact sets, where each set is
a renormalized projection of a finite union of faces of unit cubes. We exploit
this combinatorial definition to prove the connectedness of the Rauzy fractal
associated with any finite product of three-letter Arnoux-Rauzy substitutions.

27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat