Cyclic families of functions for analytic Toeplitz operators

Analytic Toeplitz operators T_φ{symbol}:f{mapping}φ{symbol}f, φ{symbol}∈H^∞, in the Hardy space H² are considered. In the case of a smooth symbol and under some assumptions of a geometric character on the curve t{mapping}φ{symbol}(e^it) a complete description of the cyclic families is obtained. This description is based on the concepts of outer function and pseudocontinuation, which, as it is known, are used for the characterization of the cyclic vectors of the direct and inverse shifts.