Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of an elliptic-difference equation related to Q4   In this paper, we investigate a nonlinear non-autonomous elliptic difference
equation, which was constructed by Ramani, Carstea and Grammaticos by
integrable deautonomization of a periodic reduction of the discrete
Krichever-Novikov equation, or Q4. We show how to construct it as a birational
mapping on a rational surface blown up at eight points in $\mathbb P^1\times
\mathbb P^1$, and find its affine Weyl symmetry, placing it in the geometric
framework of the Painlev\'e equations. The initial value space is
ell-$A_0^{(1)}$ and its symmetry group is $W(F_4^{(1)})$. We show that the
deautonomization is consistent with the lattice-geometry of Q4 by giving an
alternative construction, which is a reduction from Q4 in the usual sense. A
more symmetric reduction of the same kind provides another example of a
second-order integrable elliptic difference equation.

12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph