Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some invariants of Birkhoff billiards under conjugacy   In the class of strictly convex smooth boundaries, each of which not having
strip around its boundary foliated by invariant curves, we prove that the
Taylor coefficients of the "normalized" Mather's $\beta$-function are
invariants under $C^\infty$-conjugacies. In contrast, we prove that any two
elliptic billiard maps are $C^0$-conjugated near their respective boundaries,
and $C^\infty$-conjugated in the open cylinder, near the boundary and away from
a plain passing through the center of the underlying ellipse. We also prove
that if the billiard maps corresponding to two ellipses are topologically
conjugated then the two ellipses are similar.

29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph