Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slow invariant manifolds as curvature of the flow of dynamical systems   Considering trajectory curves, integral of n-dimensional dynamical systems,
within the framework of Differential Geometry as curves in Euclidean n-space,
it will be established in this article that the curvature of the flow, i.e. the
curvature of the trajectory curves of any n-dimensional dynamical system
directly provides its slow manifold analytical equation the invariance of which
will be then proved according to Darboux theory. Thus, it will be stated that
the flow curvature method, which uses neither eigenvectors nor asymptotic
expansions but only involves time derivatives of the velocity vector field,
constitutes a general method simplifying and improving the slow invariant
manifold analytical equation determination of high-dimensional dynamical
systems. Moreover, it will be shown that this method generalizes the Tangent
Linear System Approximation and encompasses the so-called Geometric Singular
Perturbation Theory. Then, slow invariant manifolds analytical equation of
paradigmatic Chua's piecewise linear and cubic models of dimensions three, four
and five will be provided as tutorial examples exemplifying this method as well
as those of high-dimensional dynamical systems.

20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat