# Limiting behavior of Julia sets of perturbed quadratic maps

## Robert Thijs Kozma

### (Institute for Mathematical Sciences, Mathematics Department, Stony Brook University)

Time: Tue Jun 3 13:00:00 2014

Location: Building 1, Room 114, Auditorium

Even the simplest nonlinear function *z*^{2}+*c* gives rise to chaotic dynamics resulting in very intricate mathematical objects such as the Mandelbrot and Julia sets. In this talk we first go over some basic properties of the Mandelbrot and Julia sets. We then go on to describe novel results
on the behavior of Julia sets of certain families of rational maps arising from *z*^{2}+*c* by adding a small perturbation term λ/*z*^{2} and taking the limit as λ→0. We will see that for certain *c* values the resulting Julia sets have some astonishing geometric and topological properties. Using symbolic dynamics and Cantor necklaces, we prove that as λ→0, the Julia set for this
family evolves into a space-filling fractal curve.