Homoclinic classes for generic C^1 vector fields

C. M. Carballo, C. A. Morales, Maria José Pacífico

Type: Article

Publication Date: 2003-04-01

Citations: 50

DOI: https://doi.org/10.1017/s0143385702001116

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.

Locations

Ergodic Theory and Dynamical Systems - View
arXiv (Cornell University) - View - PDF

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