Geometric Limits of Julia Sets for a Non-Hyperbolic Siegel Disk Map

Benjamin Rempfer Butler University
Faculty Sponsor(s): Scott Kaschner Butler University
The limiting behavior for sequences of filled Julia sets has been studied in several recent publications. When a non-hyperbolic degree d polynomial map f with a Siegel disk Delta is varied in the set of degree d polynomials, the limit of the filled
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

When & Where

10:45 AM
Gallahue Hall 105