THREE-DIMENSIONAL CONSERVATIVE STAR FLOWS ARE ANOSOV

被引：13

作者：

Bessa, Mario ^{[1
,2
]}

Rocha, Jorge ^{[1
]}

机构：

[1] Univ Porto, Dept Matemat Pura, P-4169007 Oporto, Portugal

[2] ESTGOH Inst Politecn Coimbra, P-3400124 Oliveira Do Hosp, Portugal

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 26卷 / 03期

关键词：

Divergence-free vector fields; Anosov flows; Dominated splitting; VOLUME;

D O I：

10.3934/dcds.2010.26.839

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A divergence-free vector field satisfies the star property if any divergence-free vector field in some C-1-neighborhood has all the singularities and all closed orbits hyperbolic. In this article we prove that any divergence-free star vector field defined in a closed three-dimensional manifold is Anosov. Moreover, we prove that a C-1-structurally stable three-dimensional conservative flow is Anosov.

引用

页码：839 / 846

页数：8

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