Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recursive structure in the definitions of gauge-invariant variables for
  any order perturbations   The construction of gauge-invariant variables for any order perturbations is
discussed. Explicit constructions of the gauge-invariant variables for
perturbations to 4th order are shown. From these explicit construction, the
recursive structure in the definitions of gauge-invariant variables for any
order perturbations is found. Through this recursive structure, the
correspondence with the fully non-linear exact perturbations is briefly
discussed.

32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs