Hypercyclic Toeplitz Operators

We study hypercyclicity of the Toeplitz operators in the Hardy space \({H^{2}(\mathbb{D})}\) with symbols of the form \({p(\overline{z}) + \varphi(z)}\), where \({p}\) is a polynomial and \({\varphi \in H^{\infty}(\mathbb{D})}\). We find both necessary and sufficient conditions for hypercyclicity which almost coincide in the case when deg \({p =1}\).