Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domains which are integrable close to the boundary and close to the
  circular ones are ellipses   The Birkhoff conjecture says that the boundary of a strictly convex
integrable billiard table is necessarily an ellipse. In this article, we
consider a stronger notion of integrability, namely integrability close to the
boundary, and prove a local version of this conjecture: a small perturbation of
an ellipse of small eccentricity which preserves integrability near the
boundary, is itself an ellipse. We generalize the result of another paper,
where integrability was proven only for specific values, proving its main
conjecture. In particular, we show that (local) integrability near the boundary
implies global integrability. One of the crucial ideas in the proof consists in
analyzing Taylor expansion of the corresponding action-angle coordinates with
respect to the eccentricity parameter, as well as using irrationality to prove
the main non-degeneracy condition.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg