Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fermi-Pasta-Ulam problem: periodic orbits, normal forms and
  resonance overlap criteria   Fermi, Pasta and Ulam observed, that the excitation of a low frequency normal
mode in a nonlinear acoustic chain leads to localization in normal mode space
on large time scales. Fast equipartition (and thus complete delocalization) in
the Fermi-Pasta-Ulam chain is restored if relevant intensive control parameters
exceed certain threshold values. We compare recent results on periodic orbits
(in the localization regime) and resonant normal forms (in a weak
delocalization regime), and relate them to various resonance overlap criteria.
We show that the approaches quantitatively agree in their estimate of the
localization-delocalization threshold. A key ingredient for this transition are
resonances of overtones.

13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph