Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nondegeneracy of heteroclinic orbits for a class of potentials on the
  plane   In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known
property, commonly used in problems involving nonlinear elliptic, parabolic or
hyperbolic P.D.E. On the other hand, Schatzman proved that in the vector case
this assumption is generic, in the sense that for any potential
$W:\mathbb{R}^m\to\mathbb{R}$, $m\geq 2$, there exists an arbitrary small
perturbation of $W$, such that for the new potential minimal heteroclinic
orbits are nondegenerate. However, to the best of our knowledge, nontrivial
explicit examples of such potentials are not available. In this paper, we prove
the nondegeneracy of heteroclinic orbits for potentials $W:\mathbb{R|^2\to
[0,\infty)$ that can be written as $W(z)=|f(z)|^2$, with $f:\mathbb{C} \to
\mathbb{C}$ a holomorphic function.

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The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: stat
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph