Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointwise existence of the Lyapunov exponent for a quasi-periodic
  equation   In this short note, we describe some recent results on the pointwise
existence of the Lyapunov exponent for certain quasi-periodic cocyles.

20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex