  We propose a general method for constructing a minimal cover of
high-dimensional chaotic attractors by embedded coherent structures, such as
(but not limited to) periodic orbits. By minimal cover we mean a subset of
available coherent structures such that the approximation of chaotic dynamics
by a minimal cover with a predefined proximity threshold is as good as the
approximation by the full available set. The proximity measure can be chosen
with considerable freedom and adapted to the properties of any given chaotic
system. In the context of a Kuramoto-Sivashinsky chaotic attractor, we
demonstrate that the minimal cover can be faithfully constructed even when the
proximity measure is defined within a subspace of dimension much smaller than
the dimension of space containing the attractor. We discuss how the minimal
cover can be used to provide a reduced description of the attractor structure
and the dynamics on it.
