A Landing Theorem for Periodic Rays of Exponential Maps
arXiv:math/0307371 · doi:10.1090/S0002-9939-06-08287-6
Abstract
We answer a question of Schleicher by showing that, for an exponential map with nonescaping singular value, every periodic ray lands. This is an analog of a theorem of Douady and Hubbard concerning polynomials. We also prove a partial converse: there are periodic external rays landing at all periodic points, with the exception of at most one periodic orbit.
10 pages, 2 figures // V4. Final Version - figures and references have been updated