Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First degree birational transformations of the Painlev\'e equations and
  their contiguity relations   We present a consistent truncation, allowing us to obtain the first degree
birational transformation found by Okamoto for the sixth Painlev\'e equation.
The discrete equation arising from its contiguity relation is then just the sum
of six simple poles. An algebraic solution is presented, which is equivalent to
but simpler than the Umemura solution. Finally, the well known confluence
provides a unified picture of all first degree birational transformations for
the lower Painlev\'e equations, ranging them in two distinct sequences.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph