Alan Sola: Potential theory and Julia sets

Complex dynamical systems were studied extensively in the early 20 th century by Fatou and Julia, who established many of the basic properties of the so-called Julia sets associated with iterated complex polynomials (or more generally, rational functions). In the 1980s, computer-generated pictures of these intriguing fractal sets became available, and their beauty helped create renewed interest in the field.

The years between seem to have been a period of less research activity. A notable exception is Hans Brolin’s doctoral thesis from the 1960 s. In his thesis, Brolin considered, among other things, potential theoretic properties of Julia sets and he proved several elegant theorems in this direction.

I will briefly review some basic material concerning potential theory and complex dynamics, and then present some of Brolin’s results.