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arXiv:math/0108226 [math.DS]AbstractReferencesReviewsResources

Homoclinic classes for generic C^1 vector fields

C. M. Carballo, C. A. Morales, M. J. Pacifico

Published 2001-08-31Version 1

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.

Comments: 17 pages
Categories: math.DS
Subjects: 37C20, 37C29
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