Benjamin Rempfer

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

*Butler University*

Julia sets always exists. It has also been shown that for all hyperbolic polynomial maps q, if fn is defined as the sum of q with a power map zn, then the same limit of the filled Julia sets exists and can be described explicitly. We attempt to extend

this convergence for the maps fn to non-hyperbolic maps q with a Siegel disk Delta and expect the theorems proved for hyperbolic polynomial maps to hold.

Mathematics & Computer Science

Oral Presentation