  While compactness is an essential assumption for many results in dynamical
systems theory, for many applications the state space is only locally compact.
Here we provide a general theory for compactifying such systems, i.e. embedding
them as invariant open subsets of compact systems. In the process we don't want
to introduce recurrence which was not there in the original system. For example
if a point lies on an orbit which remains in any compact set for only a finite
span of time then the point becomes non-wandering if we use the one-point
compactification. Instead, we develop here the appropriate theory of dynamic
compactification.
