Mathematics – Complex Variables
Scientific paper
2004-08-06
Mathematics
Complex Variables
V4 - revised version (a few typos corrected); French - accepted for publication in the Acta Mathematica Vietnamica
Scientific paper
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.
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