Homoclinic classes for generic C^1 vector fields

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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.
17 pages

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Dynamical Systems, 37C (primary); 37C20, 37C29 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/62121

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108226
 http://arxiv.org/abs/math/0108226

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arXiv