Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton flows for elliptic functions III Classification of
  $3^{\text{rd}}$ order Newton graphs   A Newton graph of order $r( \geqslant 2)$ is a cellularly embedded toroidal
graph on $r$ vertices, $2r$ edges and $r$ faces that fulfils certain
combinatorial properties (Euler, Hall). The significance of these graphs relies
on their role in the study of structurally stable elliptic Newton flows - say
$\bar{\bar{\mathcal{N}}} (f)$ - of order $r$, i.e. desingularized continuous
versions of Newton's iteration method for finding zeros for an elliptic
function $f$ (of order $r$). In previous work we established a representation
of these flows in terms of Newton graphs. The present paper results into the
classification of all $3^{\text{rd}}$ order Newton graphs, implying a list of
all nine possible $3^{\text{rd}}$ order flows $\bar{\bar{\mathcal{N}}} (f)$ (up
to conjugacy and duality).

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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex