Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of Veech groups in terms of origamis   Schmith\"usen proved in 2004 that the Veech group of an origami is closely
related to a subgroup of the automorphism group of the free group $F_2$. This
result is significant in the sense that the framework of approachable Veech
groups is greatly extended. In this paper, we continue the analysis and
consider what kind of settings of flat surfaces allow Veech groups to be
characterized combinatorially like origamis. We show that elements in the Veech
group of a flat surface with two finite Jenkins-Strebel directions are
characterized to allow a concurrence between two `origamis' defined by
geodesics in the surface. In the proof we use an observation presented by Earle
and Gardiner that a flat surface with two finite Jenkins-Strebel directions is
decomposed into a finite number of parallelograms and is proved to be of finite
analytic type. Using our results we can decide whether a matrix belongs to the
Veech group for various kinds of flat surfaces of finite analytic type.

29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th