Symbolic Dynamics & Quadratic Laminations on the Circle

In this talk, I will introduce a Collet-Eckmann type condition for the quadratic laminations on the unit circle. We will walk through the proof that this condition implies that the lamination admits a Hölder continuous conformal welding, which produces the Julia set corresponding to some unicritical polynomial \$z^2+c\$. As a consequence, we prove that almost all points on the unit circle correspond to some quadratic Julia sets that are also Hölder trees. The project is advised by Steffen Rohde.