Niel Dobbs: A random walk in exponential dynamics

Results concerning ergodic properties of maps from the exponential family f_λ : z ↦ λ exp(z) for which the Julia set is the entire complex plane were limited to two classes: Misiurewicz maps, where the orbit of zero is bounded, and maps for which the orbit of zero grows extremely fast. By modelling distributions of successive returns to the left half plane by a random walk, we can view and generalize these results in a common framework.

This work is joint with B. Skorulski.