Cyclic phenomena for composition operators on weighted Bergman spaces

Abstract

In this article, we study cyclic phenomena on the full range of weighted Bergman spaces on the right half-plane ${\mathcal{A}}_{\hat{I}}^2\pm ({\mathbb{C}}_{+}).$ We completely characterize cyclic and supercyclic composition operators induced by affine self-maps of ${\mathbb{C}}_{+},$ thereby completing the characterization of all hypercyclic, supercyclic and cyclic composition operators induced by affine symbols on ${\mathcal{A}}_{\hat{I}}^2\pm ({\mathbb{C}}_{+}).$