Abstract

In this talk we will show that in dimension greater or equal than 3 the index of a stable critical point can be any integer. More concretely, given any $k\in \; Z$ and $n\ge \; 3$ we construct a vector field on $Rn$ with a unique critical point which is stable (in positive and negative time) and has index equal to $k.$ This result extends previous ones on the index of stable critical points.