Exponential polynomials with Fatou and non-escaping sets of finite Lebesgue measure

Abstract

We give conditions ensuring that the Fatou set and the complement of the fast escaping set of an exponential polynomial $f$ have finite Lebesgue measure. Essentially, these conditions are designed such that $|f(z)|\ge \exp (|z{|}^{\alpha })$ for some $\alpha >0$ and all $z$ outside a set of finite Lebesgue measure.

18 pages, 3 figures