Local connectivity of the Julia sets of holomorphic maps with bounded type Siegel disks

Fei Yang

Let f be a holomorphic map containing an irrationally indifferent fixed point z0. If f is locally linearizable at z0, then the maximal linearizable domain containing z0 is called the Siegel disk of f centered at z0. The topology of the boundaries of Siegel disks has been studied extensively in past 3 decades. This was motivated by the prediction of Douady and Sullivan that the Siegel disk of every non-linear rational map is a Jordan domain.

http://scgp.stonybrook.edu/video_portal/video.php?id=4765

Simons- Program: Renormalization and universality in Conformal Geometry, Dynamics, Random Processes, and Field Theory