Sharif University of TechnologyScientia Iranica1026-309815620081201On the Poincare Index of Isolated Invariant Sets3080ENM.R. RazvanDepartment of Mathematics,Sharif University of TechnologyM. FotouhiDepartment of Mathematics,Sharif University of TechnologyJournal Article20090725In 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 eld are obtained
to be an isolated invariant set. As a result, the existence of innitely many homoclinic orbits for
a critical point with the Poincare index greater than one is shown.https://scientiairanica.sharif.edu/article_3080_b7d97ad9e3f8d55dbdc72e09d86c28ff.pdf