Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A dichotomy law for the Diophantine properties in $\beta$-dynamical
  systems
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat