Abstract
Given an unknown attractor A in a continuous dynamical system, how can we discover the topology and dynamics of A? 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 A onto a model systemM whose topology and dynamics are known. The complexity ofM then provides a lower bound for the complexity of A. 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 modelM can be explicitly described; and that the finite amount of information needed to construct it is computable.
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