Reconstructing the global dynamics of attractors via the Conley index

Given an unknown attractor in a continuous dynamical system, how can we discover the topology and dynamics of ? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from onto a model system whose topology and dynamics are known. The complexity of then provides a lower bound for the complexity of . The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy for a large class of attractors. The essential features of this construction are that the model can be explicitly described; and that the finite amount of information needed to construct it is computable.