Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedded surfaces with Anosov geodesic flows, approximating spherical
  billiards   We consider a billiard in the sphere S^2 with circular obstacles, and give a
sufficient condition for its flow to be uniformly hyperbolic. We show that the
billiard flow in this case is approximated by an Anosov geodesic flow on a
surface in the ambiant space S^3. As an application, we show that every
orientable surface of genus at least 11 admits an isometric embedding into S^3
(equipped with the standard metric) such that its geodesic flow is Anosov.
Finally, we explain why this construction cannot provide examples of isometric
embeddings of surfaces in the Euclidean R^3 with Anosov geodesic flows.

10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom