A Landing Theorem for Periodic Rays of Exponential Maps

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

References in corpus (4)

• Topological Dynamics of Exponential Maps on their Escaping Sets
• Classification of Escaping Exponential Maps
• Periodic Orbits, Externals Rays and the Mandelbrot Set: An Expository Account
• Parameter rays for the exponential family

Cited by in corpus (11)

• Topological Dynamics of Exponential Maps on their Escaping Sets
• Classification of Escaping Exponential Maps
• Escaping endpoints explode
• On Nonlanding Dynamic Rays of Exponential Maps
• A landing theorem for entire functions with bounded post-singular sets
• Triviality of fibers for Misiurewicz parameters in the exponential family
• Dynamic rays of bounded-type transcendental self-maps of the punctured plane
• Siegel Disks and Periodic Rays of Entire Functions
• A Landing Theorem for Periodic Dynamic Rays for Transcendental Entire Maps with Bounded Post-Singular Set
• A Converse Landing Theorem in Parameter Spaces
• A survey on MLC, Rigidity and related topics