  We introduce one dimensional sets to help describe and constrain the integral
curves of an $n$ dimensional dynamical system. These curves provide more
information about the system than the zero-dimensional sets (fixed points) do.
In fact, these curves pass through the fixed points. Connecting curves are
introduced using two different but equivalent definitions, one from dynamical
systems theory, the other from differential geometry. We describe how to
compute these curves and illustrate their properties by showing the connecting
curves for a number of dynamical systems.
