Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability of Renormalization   In the theory of renormalization for classical dynamical systems, e.g.
unimodal maps and critical circle maps, topological conjugacy classes are
stable manifolds of renormalization. Physically more realistic systems on the
other hand may exhibit instability of renormalization within a topological
class. This instability gives rise to new phenomena and opens up directions of
inquiry that go beyond the classical theory. In phase space it leads to the
coexistence phenomenon, i.e. there are systems whose attractor has bounded
geometry but which are topologically conjugate to systems whose attractor has
degenerate geometry; in parameter space it causes dimensional discrepancy, i.e.
a topologically full family has too few dimensions to realize all possible
geometric behavior.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg