On the Poincare Index of Isolated Invariant Sets

Details On the Poincare Index of Isolated Invariant Sets On the Poincare Index of Isolated Invariant Sets

2001-02-19

arxiv.org/abs/math/0102143v1

Mathematics

Dynamical Systems

Scientific paper

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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