Building Anosov flows on 3–manifolds
Building Anosov flows on 3–manifolds
复制标题
DOI：
10.2140/gt.2017.21.1837
复制
发表时间：
2014-08
影响因子：
2
通讯作者：
Franccois B'eguin;B. Yu;C. Bonatti
中科院分区：
文献类型：
--
作者：
Franccois B'eguin;B. Yu;C. Bonatti
通过将双曲集的过滤邻域粘合在一起，证明了一个允许在3流形上构造（可传递或不可传递）Anosov流的结果。我们给出了几个应用；例如：1；构造了一个同时支持可传递Anosov向量场和不可传递Anosov向量场的3流形；2. 对于任意n，我们构建一个3流形M，支持至少n个成对不同的Anosov向量场；3. 我们构造了具有指定入口叶理的传递吸引子；特别地，我们构造了一些非相干传递吸引子；4. 我们建立了一个可容纳无穷多个对非同位素横向环面的传递阿诺索夫向量场。MSC 2010: 37d20,57m。关键词：阿诺索夫流，双曲基本集，三流形。
We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting both of a transitive Anosov vector field and a non-transitive Anosov vector field; 2. for any n, we build a 3-manifold M supporting at least n pairwise different Anosov vector fields; 3. we build transitive attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive attractors; 4. we build a transitive Anosov vector field admitting infinitely many pairwise non-isotopic transverse tori. MSC 2010: 37D20, 57M. Keywords: Anosov flow, hyperbolic basic set, 3-manifold.