Abstract:

In this note we consider the exponential family $E(z)=exp(z)+c$ and show that for a large set of parameter values in its bifurcation locus, there exist rays in dynamic plane whose closure contains a pair of points separated by distance $2pi$, hence becoming nonlanding rays. We derive these parameters as limits of satellite parabolic perturbations in parameter plane, closely resembling the expositions found in the references for polynomials.