  We investigate the accelerating phases of cosmologies supported by a metric,
scalars and a single exponential scalar potential. The different solutions can
be represented by trajectories on a sphere and we find that quintessence
happens within the "arctic circle" of the sphere.
  Furthermore, we obtain multi-exponential potentials from 3D group manifold
reductions of gravity, implying that such potentials can be embedded in gauged
supergravities with an M-theory origin. We relate the double exponential case
to flux compactifications on maximally symmetric spaces and S-branes. In the
triple exponential case our analysis suggests the existence of two exotic
S(D-3)-branes in D dimensions.
