Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uses of Envelopes for Global and Asymptotic Analysis; geometrical
  meaning of renormalization group equation   We give a comprehensive review of the renormalization group method for global
and asymptotic analysis, putting an emphasis on the relevance to the classical
theory of envelopes and the existence of invariant manifolds of the dynamics
under consideration. We clarify that an essential point of the method is to
convert the problem from solving differential equations to obtaining suitable
initial (or boundary) conditions.
  We mention that the notion of envelopes is also useful for constructing
global and asymptotic behavior of wave functions of quantum systems such as the
ones with the quartic potential or double-well potential.

5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph