Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sur les points fixes et les cycles r\'epulsifs au voisinage d'une
  singularit\'e essentielle isol\'ee \`a l'instar de la m\'ethode de Zalcman   Let $g$ be a holomorphic function in the neighbourhoods of an isolated
essential singularity $v$: if $g$ omits a complex value there, then $v$ may be
approached by a sequence of repelling fixed points for $g$, whose multipliers
diverge to $\infty$. This implies that an entire function omitting a value or a
non-M\"obius self-map of the punctured plane admit infinite repelling fixed
points, whose multipliers diverge to $\infty$. By another point of view, we
show that, if $v$ is not Picard-exceptional for $g$, then $v$ can be approached
by a sequence of 2-cycles of $g$: these cycles are repelling if $v$ is not a
completely branched value.

34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th