Cyclic sets for analytic Toeplitz operators

Analytic Toeplitz operators $T_\varphi\colon f\mapsto\varphi f$, $\varphi\in H^\infty$, in the space $H^2$ are considered. In the case of smooth symbol and under some hypotheses of geometric nature on the curve $t\mapsto\varphi(e^{it})$, a full description of cyclic families is obtained. This description is based on the notions of an outer function and pseudocont: lnuation, which are employed to characterize cyclic vectors for the shift operator and its adjoint.