On Possible Limit Functions on a Fatou Component in Non-autonomous Iteration

Christopher Staniszewski, University of Rhode Island

Abstract

The Schlicht class of functions 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 functions f in the Schlicht class, there exists a subsequence of iterates of compositions of our polynomial sequence for which f is a limit function.^

Subject Area

Mathematics

Recommended Citation

Christopher Staniszewski, "On Possible Limit Functions on a Fatou Component in Non-autonomous Iteration" (2018). Dissertations and Master's Theses (Campus Access). Paper AAI10785839.
https://digitalcommons.uri.edu/dissertations/AAI10785839

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