Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical versus diffraction spectrum for structures with finite local
  complexity   It is well-known that the dynamical spectrum of an ergodic measure dynamical
system is related to the diffraction measure of a typical element of the
system. This situation includes ergodic subshifts from symbolic dynamics as
well as ergodic Delone dynamical systems, both via suitable embeddings. The
connection is rather well understood when the spectrum is pure point, where the
two spectral notions are essentially equivalent. In general, however, the
dynamical spectrum is richer. Here, we consider (uniquely) ergodic systems of
finite local complexity and establish the equivalence of the dynamical spectrum
with a collection of diffraction spectra of the system and certain factors.
This equivalence gives access to the dynamical spectrum via these diffraction
spectra. It is particularly useful as the diffraction spectra are often simpler
to determine and, in many cases, only very few of them need to be calculated.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph