  The Randall-Sundrum scenario, with a 1+3-dimensional brane in a 5-dimensional
bulk spacetime, can be generalized in various ways. We consider the case where
the Z2-symmetry at the brane is relaxed, and in addition the gravitational
action is generalized to include an induced gravity term on the brane. We
derive the complete set of equations governing the gravitational dynamics for a
general brane and bulk, and identify how the asymmetry and the induced gravity
act as effective source terms in the projected field equations on the brane.
For a Friedmann brane in an anti de Sitter bulk, the solution of the Friedmann
equation is given by the solution of a quartic equation. We find the
perturbative solutions for small asymmetry, which has an effect at late times.
