The authors suggest versions of known results on the existence, stability and smoothness of invariant manifold theory from ordinary differential equations to invariant toroidal manifolds for point mappings of an annulus in Banach spaces. The necessity of such generalization is caused by the needs of qualitative theory of differential equations with distributed parameters and by the fact that for numerous autonomous systems of partial differential equations and also delay equations, integral manifolds are invariant sets of the family of translation operators along the trajectories.