**"Poincaré-Hopf's theorem and dynamics of isolated invariant compacta"**
#### Barge, HéctorIn this talk we characterize the total index of a vector field defined in an isolating neighborhood in terms of the dynamics of the induced flow and the topology of the isolated invariant set. In this context some new versions of the Poincaré-Hopf theorem and Borsuk's antipodal theorem are given. We also see that if the isolated invariant set is non-saddle some nice consequences of these connections can be derived. This is joint work with J.M.R. Sanjurjo (Universidad Complutense de Madrid). |