California Institute of Technology >> Engineering & Applied Science

Periodic Points and Dynamic Rays of Exponential Maps

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Abstract

We investigate the dynamics of exponential maps $z\mapsto \lambda e^z$; the goal is a description by means of dynamic rays. We discuss landing properties of dynamic rays and show that in many important cases, repelling and parabolic periodic points are landing points of periodic dynamic rays. For postsingularly finite exponential maps, we use spider theory to show that a dynamic ray lands at the singular value.