Abstract. We present two results on dynamical systems. The first, due to Nam-Gyu Kang, gives a remarkable identity for Schwarzian derivatives of Riemann Mappings from the upper half plane to the exterior of SLE traces. The second result (joint work with Ilia Binder) is a strong approximation theorem for the f(alpha) spectrum for arbitrary planar domains (with respect to harmonic measure), where the approximation is by hyperbolic or "Pure Cantor" Julia Sets. We also make some speculations about both of these problems.