Dynamics for affine composition operators on weighted Bergman space of a half plane

In this article, we completely characterize the positive expansive and absolutely Cesàro composition operators $C_{\phi }f=f\circ \phi$ induced by affine self-maps $\phi$ of the right half-plane ${\mathbb{C}}_{+}$ on the weighted Bergman space ${\mathcal{A}}_{\alpha }^2({\mathbb{C}}_{+})$. Furthermore, we characterize which of these operators have the positive shadowing property.