The Conley Index over a Base

  title={The Conley Index over a Base},
  author={Marian Mrozek and JAMES F. REINECK},
We construct a generalization of the Conley index for flows. The new index preserves information which in the classical case is lost in the process of collapsing the exit set to a point. The new index has most of the properties of the classical index. As examples, we study a flow with a knotted orbit in R3, and the problem of continuing two periodic orbits which are not homotopic as loops. 

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