Date of Award
Doctor of Philosophy in Mathematics
The Schlicht class of functions, commonly denoted as S, is the class of univalent functions defined on the unit disk such that f (0) = 0 and f’(0) = 1. This is a well-studied class for which many results are known. We prove that there exists a bounded sequence of polynomials, and a Fatou component for this sequence, such that for all f ∈ S, there exists a subsequence of iterates of compositions of our polynomial sequence for which f is a limit function.
Staniszewski, Christopher, "On Possible Limit Functions on a Fatou Component in Non-Autonomous Iteration" (2018). Open Access Dissertations. Paper 724.