A model for boundary dynamics of Baker domains

Abstract

We consider the transcendental entire function f(z)=z+e−z, which has a doubly parabolic Baker domain U of degree two, i.e. an invariant stable component for which all iterates converge locally uniformly to infinity, and for which the hyperbolic distance between successive iterates converges to zero. It is known from general results that the dynamics on the boundary is ergodic and recurrent and that the set of points in ∂U whose orbit escapes to infinity has zero harmonic measure.