**abstract:**
How many nonrepelling cycles can a transcendental map $f$
have? We will give a combinatorial proof of the classical
Fatou-Shishikura inequality for transcendental maps, under the
assumption that periodic rays land. The classical version gives a
bound on the number of nonrepelling cycles in terms of the number of
'singular values'. Our inequality will include repelling periodic
orbits which are not landing point of any periodic ray.

Wed 17 Oct, 15:30 - 16:30, Sala Conferenze Centro De Giorgi

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