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On the Poincare Index of Isolated Invariant Sets

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...

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Bibliographic Details
Published in:arXiv.org 2001-02
Main Authors: Razvan, M R, M Fotouhi Firoozabad
Format: Article
Language:English
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Online Access:Get full text
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Summary: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.
ISSN:2331-8422