Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase-Transition Theory of Instabilities. III. The Third-Harmonic
  Bifurcation on the Jacobi Sequence and the Fission Problem   In Papers I and II, we have used a free-energy minimization approach that
stems from the Landau-Ginzburg theory of phase transitions to describe in
simple and clear physical terms the secular and dynamical instabilities as well
as the bifurcations along equilibrium sequences of rotating, self-gravitating
fluid systems. Here we investigate the secular and dynamical 3rd-harmonic
instabilities that appear first on the Jacobi sequence of incompressible zero-
vorticity ellipsoids. Poincare found a bifurcation point on the Jacobi sequence
where a 3rd-harmonic mode becomes neutral. A sequence of pear-shaped equilibria
branches off at this point but stands at higher energies. Therefore, the Jacobi
ellipsoids remain secularly and dynamically stable. Cartan found that dynamical
3rd-harmonic instability also sets in at the Jacobi-pear bifurcation. We find
that Cartan's instability leads to differentially rotating objects and not to
uniformly rotating pear-shaped equilibria. We demonstrate that the pear-shaped
sequence exists at higher energies and at higher rotation relative to the
Jacobi sequence. The Jacobi ellipsoid undergoes fission on a secular time scale
and a short-period binary is produced. The classical fission hypothesis of
binary-star formation of Poincare and Darwin is thus feasible.

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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc