Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A catalogue of singularities   This paper is an attempt to classify finite-time singularities of PDEs. Most
of the problems considered describe free-surface flows, which are easily
observed experimentally. We consider problems where the singularity occurs at a
point, and where typical scales of the solution shrink to zero as the
singularity is approached. Upon a similarity transformation, exact self-similar
behaviour is mapped to the fixed point of a {\it infinite dimensional dynamical
system} representing the original dynamics. We show that the dynamics close to
the fixed point is a useful way classifying the structure of the singularity.
Specifically, we consider various types of stable and unstable fixed points,
centre-manifold dynamics, limit cycles, and chaotic dynamics.

11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics