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Homoclinic classes for generic C^1 vector fields

  • C. M. CARBALLO (a1), C. A. MORALES (a2) and M. J. PACIFICO (a2)
  • DOI: http://dx.doi.org/10.1017/S0143385702001116
  • Published online: 01 September 2003
Abstract

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 it is the intersection of its stable set with its unstable set. All these properties are well known for structurally stable Axiom A vector fields.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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