Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A classification of aperiodic order via spectral metrics and Jarn\'ik
  sets   Given an $\alpha > 1$ and a $\theta$ with unbounded continued fraction
entries, we characterise new relations between Sturmian subshifts with slope
$\theta$ with respect to (i) an $\alpha$-H\"oder regularity condition of a
spectral metric, (ii) level sets defined in terms of the Diophantine properties
of $\theta$, and (iii) complexity notions which we call $\alpha$-repetitive,
$\alpha$-repulsive and $\alpha$-finite; generalisations of the properties known
as linearly repetitive, repulsive and power free, respectively. We show that
the level sets relate naturally to (exact) Jarn\'{\i}k sets and prove that
their Hausdorff dimension is $2/(\alpha + 1)$.

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The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat