Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponentially small heteroclinic breakdown in the generic Hopf-zero
  singularity   In this paper we prove the breakdown of an heteroclinic connection in the
analytic versal unfoldings of the generic Hopf-Zero singularity in an open set
of the parameter space. This heteroclinic orbit appears at any order if one
performs the normal form around the origin, therefore it is a phenomenon
"beyond all orders". In this paper we provide a formula for the distance
between the corresponding stable and unstable one dimensional manifolds which
is given by an exponentially small function in the perturbation parameter. Our
result applies both for conservative and dissipative unfoldings.

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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: stat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph