  Using the thin-shell formalism we discuss the motion of domain walls in de
Sitter and anti-de Sitter (AdS) time-dependent bulks. This motion results in a
dynamics for the brane scale factor. We show that in the case of a clean brane
the scale factor describes both singular and non-singular universes, with
phases of contraction and expansion. These phases can be understood as
quotients of AdS spacetime by a discrete symmetry group. We discuss this effect
in some detail, and suggest how the AdS/CFT correspondence could be applied to
obtain a non perturbative description of brane-world string cosmology.
