Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global dynamics of stationary, dihedral, nearly-parallel vortex
  filaments   The goal of this paper is to give a detailed analytical description of the
global dynamics of N points interacting through the singular logarithmic
potential and subject to the following symmetry constraint: at each instant
they form an orbit of the dihedral group of order 2l. The main device in order
to achieve our results is a technique very popular in Celestial Mechanics,
usually referred to as "McGehee transformation". After performing this change
of coordinates that regularizes the total collision, we study the rest-points
of the flow, the invariant manifolds and we derive interesting information
about the global dynamics for l=2. We observe that our problem is equivalent to
studying the geometry of stationary configurations of nearly-parallel vortex
filaments in three dimensions in the LIA approximation.

34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex