  We undertake a systematic exploration of recurrent patterns in a
1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather
turbulent system, the long-time dynamics takes place on a low-dimensional
invariant manifold. A set of equilibria offers a coarse geometrical partition
of this manifold. A variational method enables us to determine numerically a
large number of unstable spatiotemporally periodic solutions. The attracting
set appears surprisingly thin - its backbone are several Smale horseshoe
repellers, well approximated by intrinsic local 1-dimensional return maps, each
with an approximate symbolic dynamics. The dynamics appears decomposable into
chaotic dynamics within such local repellers, interspersed by rapid jumps
between them.
