2001/08/31 by C. M. Carballo, Carballo, C. M., C. A. Morales +4
Mathematics · #37C (primary) #37C20 #37C29 (secondary) #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis #math.DS #msc:37C #msc:37C20 #msc:37C29
paper · pdf · doi:10.48550/arxiv.math/0108226
17 pages
arxiv created 2001/08/31 · openalex publication_date 2001/08/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that homoclinic classes for a residual set of C1 vector fields X on closed n-manifolds are maximal transitive and depend continuously on periodic orbit data. In addition, X does not exhibit cycles formed by homoclinic classes. We also prove that a homoclinic class of X is isolated if and only if it is Omega-isolated, and that it is the intersection of its stable set and its unstable set. All these properties are well known for structurally stable Axiom A vector fields.