  In this work, we study the dynamical properties of Krystyna Kuperberg's
aperiodic flows on $3$-manifolds. We introduce the notion of a ``zippered
lamination'', and with suitable generic hypotheses, show that the unique
minimal set for such a flow is an invariant zippered lamination. We obtain a
precise description of the topology and dynamical properties of the minimal
set, including the presence of non-zero entropy-type invariants and chaotic
behavior. Moreover, we show that the minimal set does not have stable shape,
yet satisfies the Mittag-Leffler condition for homology groups.
