Prescribing the postsingular dynamics of meromorphic functions

Date:
18.03.19
Times:
10:00 to 11:00
Place:
IMUB-Universitat de Barcelona
Speaker:
Kirill Lazebnik
University:
Caltech

Abstract

We show that any dynamics on any discrete planar sequence $S$ can be realized by the postsingular dynamics of some meromorphic function, provided we allow for small perturbations of $S$. This work was influenced by an analogous result of DeMarco, Koch and McMullen for finite $S$ in the rational setting. The proof contains a method for constructing meromorphic functions with good control over both the postsingular set of $f$ and the geometry of $f$, using the Folding Theorem of Bishop and a classical fixpoint theorem. This is joint work with Christopher Bishop.