Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical three rotor problem: periodic solutions, stability and chaos   This paper concerns the classical dynamics of three coupled rotors: equal
masses moving on a circle subject to attractive cosine inter-particle
potentials. It is a simpler variant of the gravitational three-body problem and
also arises as the classical limit of a model of coupled Josephson junctions.
Unlike in the gravitational problem, there are no singularities (neither
collisional nor non-collisional), leading to global existence and uniqueness of
solutions. In appropriate units, the non-negative energy $E$ of the relative
motion is the only free parameter. We find analogues of the Euler-Lagrange
family of periodic solutions: pendulum and isosceles solutions at all energies
and choreographies up to moderate energies. The model displays
order-chaos-order behavior: it is integrable at zero and infinitely high
energies but displays a fairly sharp transition from regular to chaotic
behavior as $E$ is increased beyond $E_c \approx 4$ and a more gradual return
to regularity. The transition to chaos is manifested in a dramatic rise of the
fraction of the area of the Hill region of Poincar\'e surfaces occupied by
chaotic sections and also in the spontaneous breaking of discrete symmetries of
Poincar\'e sections present at lower energies. Interestingly, the above
pendulum solutions alternate between being stable and unstable, with the
transition energies cascading geometrically from either side at $E = 4$. The
transition to chaos is also reflected in the curvature of the Jacobi-Maupertuis
metric that ceases to be everywhere positive when $E$ exceeds four. Examination
of Poincar\'e sections also indicates global chaos in a band of energies $(5.33
\lesssim E \lesssim 5.6)$ slightly above this transition.

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The categories of this paper are: astro-ph
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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: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an