Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics on an infinite surface with the lattice property   Dynamical systems on an infinite translation surface with the lattice
property are studied. The geodesic flow on this surface is found to be
recurrent in all but countably many rational directions. Hyperbolic elements of
the affine automorphism group are found to be nonrecurrent, and a precise
formula regarding their action on cylinders is proven. A deformation of the
surface in the space of translation surfaces is found, which "behaves nicely"
with the geodesic flow and action of the affine automorphism group.

9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph