Seminar

To participate in this seminar, please register HERE.

Transcendental entire maps from class S (also called Speiser class or maps of finite type) share several common properties with polynomials. This includes functional-theoretical aspects such as a similar structure of the singular set, as well as dynamical aspects, for example, the no-wandering-domains theorem, etc. 

In this talk, I will try to explain how we can look at maps from class S as limits of polynomial maps, and which dynamical meaning these approximations may have. I will start with speaking about one of the best known cases: considering exponential maps as limits of uncritical polynomials; I will state what it implies for parameter and dynamical planes of these functions. Further, I will provide a few more general results and, finally, will speak about how we hope to construct "dynamically meaningful" polynomial approximations for arbitrary maps in class S using planar embedded graphs. This is joint work with Malavika Mukundan and Bernhard Reinke.