Homoclinic classes for generic C1 vector fields

被引：37

作者：

Carballo, CM

Morales, CA

Pacifico, MJ

机构：

[1] Pontificia Univ Catolica Rio de Janeiro, Dept Matemat, BR-22453900 Rio de Janeiro, Brazil

[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, Brazil

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2003年 / 23卷

关键词：

D O I：

10.1017/S0143385702001116

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Ohm-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.

引用

页码：403 / 415

页数：13

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