  We describe the approximation of a continuous dynamical system on a p. l.
manifold or Cantor set by a tractable system. A system is tractable when it has
a finite number of chain components and, with respect to a given full
background measure, almost every point is generic for one of a finite number of
ergodic invariant measures. The approximations use non-degenerate simplicial
dynamical systems for p. l. manifolds and shift-like dynamical systems for
Cantor Sets.
