Conley index

Summary

The Conley index is a topological invariant attached to an isolated invariant set of a flow. It is the homotopy type of a pointed space obtained from a compact neighbourhood by collapsing the part through which orbits leave. It extends the Morse index of a nondegenerate critical point to invariant sets that may be large and complicated. The index is unchanged under small perturbations of the flow, and a nontrivial index proves that the invariant set is nonempty.