Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral analysis of a family of binary inflation rules   The family of primitive binary substitutions defined by $1 \mapsto 0 \mapsto
0 1^m$ with $m\in\mathbb{N}$ is investigated. The spectral type of the
corresponding diffraction measure is analysed for its geometric realisation
with prototiles (intervals) of natural length. Apart from the well-known
Fibonacci inflation ($m=1$), the inflation rules either have integer inflation
factors, but non-constant length, or are of non-Pisot type. We show that all of
them have singular diffraction, either of pure point type or essentially
singular continuous.

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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys