Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension reduction for slow-fast, piecewise-smooth, continuous systems
  of ODEs   The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems
of ODEs occurs on critical manifolds that are piecewise-linear. At points of
non-differentiability, such manifolds are not normally hyperbolic and so the
fundamental results of geometric singular perturbation theory do not apply. In
this paper it is shown that if the critical manifold is globally stable then
the system is forward invariant in a neighbourhood of the critical manifold. It
follows that in this neighbourhood the dynamics is given by a regular
perturbation of the dynamics on the critical manifold and so dimension
reduction can be achieved. If the attraction is instead non-global, additional
dynamics involving canards may be generated. For boundary equilibrium
bifurcations of piecewise-smooth, continuous systems, the results are used to
establish a general methodology by which such bifurcations can be analysed.
This approach is illustrated with a three-dimensional model of ocean
circulation.

27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph