1. Departament de Matemàtiques & IMAC, Universitat Jaume I, E‐12071 Castelló, Spain;2. Mathematical Institute, University of Paderborn, 33095 Paderborn, Germany. Phone: +49?5251?60?2606, Fax: +49 5251 60 3836
Abstract:
We consider analytic self‐maps φ on $mathbf {D}$ and prove that the composition operator Cφ acting on $H_{v}^0$ is hypercyclic if φ is an automorphism or a hyperbolic non‐automorphic symbol with no fixed point. We give examples of weights v and parabolic non‐automorphisms φ on $mathbf {D}$ which yield non‐hypercyclic composition operators Cφ on $H_{v}^0$.