Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On conjugacy of convex billiards   Given a strictly convex domain $\Omega$ in $\R^2$, there is a natural way to
define a billiard map in it: a rectilinear path hitting the boundary reflects
so that the angle of reflection is equal to the angle of incidence. In this
paper we answer a relatively old question of Guillemin. We show that if two
billiard maps are $C^{1,\alpha}$-conjugate near the boundary, for some $\alpha
> 1/2$, then the corresponding domains are similar, i.e. they can be obtained
one from the other by a rescaling and an isometry. As an application, we prove
a conditional version of Birkhoff conjecture on the integrability of planar
billiards and show that the original conjecture is equivalent to what we call
an "Extension problem". Quite interestingly, our result and a positive solution
to this extension problem would provide an answer to a closely related question
in spectral theory: if the marked length spectra of two domains are the same,
is it true that they are isometric?

7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs