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1999 | 47 | 1 | 145-156
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Reconstructing the global dynamics of attractors via the Conley index

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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 system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 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 model 𝓜 can be explicitly described; and that the finite amount of information needed to construct it is computable.
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  • Institute for Dynamics, Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025, U.S.A.
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