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

#### 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.

http://digitalcommons.uri.edu/dissertations/AAI10785839