Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentiability of Mather's average action and integrability on closed
  surfaces   In this article we study the differentiability of Mather's $\beta$-function
on closed surfaces and its relation to the integrability of the system.

7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat