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Recent symmetry considerations [Flach et al., Phys. Rev. Lett. 84, 2358 (2000)] have shown that dc currents may be generated in the stochastic layer of a system describing the motion of a particle in a one-dimensional potential in the presence of an ac time-periodic drive. In this paper we explain the dynamical origin of this current. We show that the dc current is induced by the presence and desymmetrization of ballistic channels inside the stochastic layer. The existence of these channels is due to resonance islands with nonzero winding numbers. The characterization of the flight dynamics inside ballistic channels is described by distribution functions. We obtain these distribution functions numerically and find very good agreement with simulation data.