Preprint A205/2003
Homoclinic classes for generic C^1 vector fields
M. J. Pacifico | Carballo, C. M. | Morales, C. A.
Keywords: homoclinic classes
We prove that homoclinic classes for a residual set of C^1 vector fields on closed n-dimensional manifolds are maximal transitive, and depende continously on periodic orbit data. In addition, X does not exhibit cycles formed by homoclinic classes. We also prove that a homoclinic class is isolated if and only if it is Omega-isolated, and it is the intersection of its stable set with its unstable set. All these properties are well known for structural stable Axiom A flows.