Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on Joachimsthal integral and Poritsky property   The billiard in an ellipse has an integral linear in momentum, the
Joachimsthal integral. We show that the existence of such an integral
characterizes conics. We extend this result to the spherical and hyperbolic
geometries and to higher dimensions. We connect the existence of Joachimsthal
integral with the Poritsky property, a property of billiard curves, called so
after H. Poritsky whose important 1950 paper was one of the early studies of
the billiard problem.

1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org