Homoclinic classes for generic C^1 vector fields

Details Homoclinic classes for generic C^1 vector fields Homoclinic classes for generic C^1 vector fields

2001-08-31

arxiv.org/abs/math/0108226v1

Mathematics

Dynamical Systems

17 pages

Scientific paper

We prove that homoclinic classes for a residual set of C^1 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.

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