Simplicial Models for the Global Dynamics of Attractors

Given an unknown attractor in a continuous dynamical system, how we can 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 . In this paper, we use the techniques of the Conley index 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.