We introduce index systems, a tool for studying isolated invariant sets of
dynamical systems that are not necessarily hyperbolic. The mapping of the index
systems mimics the expansion and contraction of hyperbolic maps on the tangent
space, and they may be used like Markov partitions to generate symbolic
dynamics. Every continuous dynamical system satisfying a weak form of
expansiveness possesses an index system. Because of their topological
robustness, they can be used to obtain rigorous results from computer
approximations of a dynamical system.