On the Poincare Index of Isolated Invariant Sets
Abstract
In this paper, we use Conley index theory to examine the Poincare index of an isolated invariant set. We obtain some limiting conditions on a critical point of a planar vector field to be an isolated invariant set. As a result we show the existence of infinitely many homoclinic orbits for a critical point with the Poincare index greater than one.
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