Connected Simple Systems and the Conley Index of Isolated Invariant Sets.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The Conley index is an extremely useful tool for the study of structural properties of isolated invariant sets such as critical points or periodic solutions in local flows. Teh continuation theorem shows that the properties of the flow which are described by the Conley index are among those which are invariant under perturbations. This is a fact of great interest in many applications. Most of the results in the present paper are not new. The object of this work is to give a self-contained presentation of most of the basic concepts and theorems in the index theory for flows which can otherwise only be found in a number of different papers. Moreover, we have simplified a number of the complicated proofs.
- Theoretical Mathematics
- Fluid Mechanics