Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely invariant sets of normality for rational semigroups   Let G be a semigroup of rational functions of degree at least two where the
semigroup operation is composition of functions. We prove that the largest open
subset of the Riemann sphere on which the semigroup G is normal and is
completely invariant under each element of G, can have only 0, 1, 2, or
infinitely many components.

20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat