On the dynamics of Toeplitz operators over Bergman spaces

We investigate the hypercyclicity of Toeplitz operators on the Bergman space $L_{A}^{2}(\mathbb{D})$ with symbols of the form $Ψ(z) = γ\bar{z}+ψ(z)$, where $γ\in \mathbb{C} \setminus \{0\}$ and $ψ$ is analytic on an open neighborhood of the closed unit disc $\overline{\mathbb{D}}$. Our approach bypa