Sur les points fixes et les cycles répulsifs au voisinage d'une singularité essentielle isolée à l'instar de la méthode 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-Möbius 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-exceptiona