On the Poincare Index of Isolated Invariant Sets


Department of Mathematics,Sharif University of Technology


In this paper, the Conley index theory is used to examine the Poincare index of an isolated
invariant set. Some limiting conditions on a critical point of a planar vector eld are obtained
to be an isolated invariant set. As a result, the existence of in nitely many homoclinic orbits for
a critical point with the Poincare index greater than one is shown.