On the Poincare Index of Isolated Invariant Sets

2001/02/19 by M. R. Razvan, Razvan, M. R., M. Fotouhi Firoozabad +1
Mathematics · #37B30 #37C29 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DS #msc:37B30 #msc:37C29

paper · pdf · doi:10.48550/arxiv.math/0102143

arxiv created 2001/02/19 · openalex publication_date 2001/02/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

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