On the Poincare Index of Isolated Invariant Sets
Dynamical Systems
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0102143,
title = {On the Poincare Index of Isolated Invariant Sets},
author = {M. R. Razvan and M. Fotouhi Firoozabad},
journal= {arXiv preprint arXiv:math/0102143},
year = {2007}
}