Mats Bylund: Sinai's principle in complex dynamics

Abstract: We will discuss Sinai's principle for recurrence in the unicritical dynamics from the point of view of harmonic measure. In
particular we show that for almost all \(c\) with respect to the harmonic measure on the boundary of the Mandelbrot set, \(\vert f_c^n(c) - c \vert \leq n^{-a}\) infinitely often if and only if \(a<1\).

This talk is based on joint work with Graczyk and Świątek.