Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry and dynamics of billiards in symmetric phase space   The billiard problem of statistical physics is considered in a new geometric
approach with a symmetric phase space. The structure and topological features
of typical billiard phase portrait are defined. The connection between
geometric, dynamic and statistic properties of smooth billiard is established.
Other directions of the theory on development are pointed out.

2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
16
The categories of this paper are: stat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an