About Rays, Dreadlocks and Periodic Points in Transcendental Dynamics

Abstract

We study some aspects of the iteration of an entire map f over the complex plane ℂ. In many settings in complex dynamics one can define periodic curves (called dynamic rays) in the dynamical plane and study their relation with periodic points. The most famous example of this kind of results is the Douady-Hubbard landing theorem for polynomial dynamics. We describe an analogous statements for transcendental maps which satisfy some growth conditions and a further generalization to general transcendental maps with bounded postsingular set, without any growth assumption. We also describe some implications for rigidity. The results described here are from a joint work with Lasse Rempe-Gillen.