Alex Glickfield *Butler University*

**Faculty Sponsor(s): **Scott Kaschner *Butler University*

When an analytic function from the complex unit disk to itself is iterated (i.e. composed with itself), the sequence of iterates will converge to a point in the closed unit disk. The point of convergence is known as the Denjoy-Wolff point. In this talk, we examine analytic functions which converge uniformly to a boundary Denjoy-Wolff point. We will prove that, under an iterative process, the closed unit disk maps to a subset of the unit disk union the Denjoy-Wolff point.

Mathematics & Computer Science