Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-field limits of phase oscillator networks and their symmetries   Rather than considering a large collection of interacting dynamical nodes on
a graph, one typically considers a continuous limit to understand the dynamics.
Depending on the type of network under consideration, different continuum
descriptions may be appropriate: Sometimes, it is sufficient to track the
evolution of a distribution of states, sometimes, one wants to track the state
of a particular node. Here, we explicitly analyze the symmetry properties of
inifinite-dimensional continuum descriptions of phase oscillator networks.
While symmetries and their consequences have been widely studied for finite
network dynamical systems, much less is known about their continuous limits. We
come across some phenomena that have no finite-dimensional counterpart, such as
noninvertible symmetries. Our insights allow us to identify different
continuous limits as invariant subspaces within a single dynamical framework.
While we focus on phase oscillator networks, our results also apply to other
dynamical systems on graph limits.

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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas