Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spontaneous Breaking of Classical PT Symmetry   The classical trajectories of the family of complex PT-symmetric Hamiltonians
$H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex
orbits that have been studied in the past are PT symmetric (left-right
symmetric). The periods of these orbits exhibit an unusual dependence on the
parameter $\epsilon$. There are regions in $\epsilon$ of smooth behavior
interspersed with regions of rapid variation. It is demonstrated that the onset
of rapid variation is associated with strange new kinds of classical
trajectories that have never been seen previously. These rare kinds of
trajectories are not PT symmetric and occur only for special rational values of
$\epsilon$.

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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph