1 9 Fe b 20 01 On the Poincaré Index of Isolated Invariant Sets
نویسندگان
چکیده
In this paper, we use Conley index theory to examine the Poincaré 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 Poincaré index greater than one.
منابع مشابه
The Conley Index for Decompositionsof Isolated Invariant Sets 1
Let f be a continuous map of a locally compact metric space X into itself. Suppose that S is an isolated invariant set with respect to f being a disjoint union of a xed nite number of compact sets. We deene an index of Conley type for isolated invariant sets admitting such a decomposition and prove some of its properties, which appear to be similar to that of the ordinary Conley index for maps....
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