# Families of rational maps and dynamics

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Xavier Buff

created by risa on 14 Feb 2018

20 feb 2018
-- 16:00

Aula D'Antoni, Dip.Matematica, Università "Tor Vergata", Roma

**Abstract.**

Given integers $d\geq 2$ and $2\leq k\leq 2d-2$, the family of rational maps of degree $d$ having $k$ distinct critical points is a smooth quasiprojective variety. We shall present results and open questions regarding subvarieties where some of the critical points are periodic.
Are those subvarieties smooth, do they intersect transverally, how many connected components do they have, how do they distribute as the period tend to infinity?