Revista Matemática Iberoamericana


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Volume 32, Issue 1, 2016, pp. 267–274
DOI: 10.4171/RMI/886

Published online: 2016-02-29

A note on repelling periodic points for meromorphic functions with a bounded set of singular values

Anna Miriam Benini[1]

(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. Iberoamericana 32 (2016), 267-274. doi: 10.4171/RMI/886