Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Pressure and the Variational Principle of Noncompact Sets
  for Amenable Group Actions   The notion of topological pressure was introduced by Ruell and also he
formulated a variational principle for the topological pressure. Pesin and
Pitskel introduced a definition of topological on subsets inspired by Hausdorff
dimension. In this paper, we considered the topological pressure of a
noncompact subset for amenable group actions and showed that under the tempered
condition, we get the variational principle for topological pressure.

8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom