Department of Mathematics,Sharif University of Technology
Abstract
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.
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