Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diophantine property of matrices and attractors of projective iterated
  function systems in $\mathbb{RP}^1$   We prove that almost every finite collection of matrices in
$GL_d(\mathbb{R})$ and $SL_d(\mathbb{R})$ with positive entries is Diophantine.
Next we restrict ourselves to the case $d=2$. A finite set of
$SL_2(\mathbb{R})$ matrices induces a (generalized) iterated function system on
the projective line $\mathbb{RP}^1$. Assuming uniform hyperbolicity and the
Diophantine property, we show that the dimension of the attractor equals the
minimum of 1 and the critical exponent.

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The categories of this paper are: q-alg
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an