Revista Matemática Iberoamericana
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Published online: 2016-02-29
A note on repelling periodic points for meromorphic functions with a bounded set of singular valuesAnna Miriam Benini (1) Università di Roma 'Tor Vergata', Italy
Let $f$ be a meromorphic function with a bounded set of singular values and for which infinity is a logarithmic singularity. Then we show that f has infinitely many repelling periodic points for any minimal period $n ≥ 1$, using a much simpler argument than the corresponding results for arbitrary entire transcendental functions.
Keywords: Meromorphic functions, entire functions, logarithmic coordinates, holomorphic dynamics, transcendental functions, repelling periodic points
Benini Anna Miriam: A note on repelling periodic points for meromorphic functions with a bounded set of singular values. Rev. Mat. Iberoam. 32 (2016), 267-274. doi: 10.4171/RMI/886