Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrical Theory of Separation of Variables, a review of recent
  developments   The Separation of Variables theory for the Hamilton-Jacobi equation is 'by
definition' related to the use of special kinds of coordinates, for example
Jacobi coordinates on the ellipsoid or St\"ackel systems in the Euclidean
space. However, it is possible and useful to develop this theory in a
coordinate-independent way: this is the Geometrical Theory of Separation of
Variables. It involves geometrical objects (like special submanifolds and
foliations) as well as special vector and tensor fields like Killing vectors
and Killing two-tensors (i.e. isometries of order one and two), and their
conformal extensions; quadratic first integrals are associated with the Killing
two-tensors. In the recent years Separable Systems provide mathematical
structures studied from different points of view. We present here a short
review of some of these structures and of their applications with particular
consideration to the underlying geometry. Algebraic relations among Killing
tensors, quadratic first integrals or their associated second order
differential operators and some aspects of approximation with separable systems
are considered. This paper has been presented as a poster at Dynamics Days
Europe 2008, Delft 25-29 August 2008.

35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn