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On the Poincare Index of Isolated Invariant Sets

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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 field are obtained to be an isolated invariant set. As a result, the existence of infinitely many homoclinic orbits for a critical point with the Poincare index greater than one is shown.

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