Abstract:

Following Eremenko's conjecture, we study the existence of dynamic rays for transcendental functions. Recently Lasse Rempe et al. gave a positive answer to this question for functions in class $mathcal B$ of finite order. I will sketch the proof of this result and I will explain how this can be extended to holomorphic self-maps of the punctured plane $mathbb C^*=mathbb Csetminus {0}$.