Dynamics Seminar

Stefanie Hittmeyer

(University of Auckland)

"Generalised Mandelbrot and Julia sets in a nonanalytic perturbation of the quadratic family"


Date: Tue, May 24, 2016
Time: 14:15
Place: Research I Seminar Room

Abstract: We consider a nonanalytic perturbation of the complex quadratic family that is associated to wild Lorenz-like chaos. The perturbation opens up the critical value to a disk and saddle points and their stable and unstable sets appear. These sets interact with the generalised Julia set, leading to the (dis)appearance of chaotic attractors and to generalised Julia sets in the form of Cantor bouquets, Cantor tangles and Cantor cheeses. A generalised version of the Mandelbrot set encodes the conjectured trichotomy.