Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase oscillators with global sinusoidal coupling evolve by Mobius group
  action   Systems of N identical phase oscillators with global sinusoidal coupling are
known to display low-dimensional dynamics. Although this phenomenon was first
observed about 20 years ago, its underlying cause has remained a puzzle. Here
we expose the structure working behind the scenes of these systems, by proving
that the governing equations are generated by the action of the Mobius group, a
three-parameter subgroup of fractional linear transformations that map the unit
disc to itself. When there are no auxiliary state variables, the group action
partitions the N-dimensional state space into three-dimensional invariant
manifolds (the group orbits). The N-3 constants of motion associated with this
foliation are the N-3 functionally independent cross ratios of the oscillator
phases. No further reduction is possible, in general; numerical experiments on
models of Josephson junction arrays suggest that the invariant manifolds often
contain three-dimensional regions of neutrally stable chaos.

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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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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: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: stat