DSNT Seminar: Sinai's principle in complex dynamic

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, $\vert f_c^n(c) - c \vert \leq 1/n^\alpha$ infinitely often if and only if $\alpha \leq 1$.

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

This is a seminar in our seminar series on Dynamical Systems and Number Theory (DSNT).