  A matchbox manifold is a connected, compact foliated space with totally
disconnected transversals; or in other notation, a generalized lamination. It
is said to be Lipschitz if there exists a metric on its transversals for which
the holonomy maps are Lipschitz. Examples of Lipschitz matchbox manifolds
include the exceptional minimal sets for $C^1$-foliations of compact manifolds,
tiling spaces, the classical solenoids, and the weak solenoids of McCord and
Schori, among others. We address the question: When does a Lipschitz matchbox
manifold admit an embedding as a minimal set for a smooth dynamical system, or
more generally for as an exceptional minimal set for a $C^1$-foliation of a
smooth manifold? We gives examples which do embed, and develop criteria for
showing when they do not embed, and give examples. We also discuss the
classification theory for Lipschitz weak solenoids.
