| Affiliation: | Instytut Informatyki, Uniwersytet Jagiellonski, 30-072 Kraków, Poland ; Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14214-3093 ; Instytut Matematyki, Uniwersytet Jagiellonski, 30-059 Kraków, Poland |
| Abstract: | 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  , and the problem of continuing two periodic orbits which are not homotopic as loops. |
