Dynamical approximations of postsingularly finite entire maps

Entire functions with finitely many singular values share many dynamical features with polynomials. This is even more the case in the setting of postsingularly finite (psf) functions, here there is not only a finite set of singular values, but every singular value also has a finite orbit.

I will give a brief overview of the dynamics of psf entire functions and show how to approximate psf entire functions by psf polynomials. The main tool is a combinatorial convergence of topological models related to Thurston's classification of branched covers.

This is based on joint work with Malavika Mukundan and Nikolai Prochorov.