Anosov flows on new three manifolds
Anosov flows on new three manifolds
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DOI：
10.1007/bf01390039
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发表时间：
1980-06
影响因子：
3.1
通讯作者：
M. Handel;W. Thurston
中科院分区：
文献类型：
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作者：
M. Handel;W. Thurston
在本文中，Anosov流~ t: M~ M是体积守恒的（根据Franks和Williams最近的例子，这是一个非平凡的假设），它们的周围流形M是紧致的、可定向的和三维的。我们的目的是给出一个简单的构造，它可以产生一系列光滑的、非代数的（定义如下）Anosov流。在给定流形m3上存在保体积的Anosov流有直接的推论。稳定叶和不稳定叶分别为余维1和极小叶。如果必要的话，通过重新参数化9，强稳定和强不稳定叶理所产生的流（称为环流）也是最小的。因此我们有了关系
Throughout this paper, Anosov flows~ t: M~ M are volume preserving (a nontrivial assumption in light of Franks and Williams' recent example), and their ambient manifolds M are compact, orientable and three dimensional. Our purpose is to present a simple construction that yields a family of C smooth, nonalgebraic (definitions below) Anosov flows. The existence of a volume-preserving Anosov flow~ on a given manifold M 3 has immediate corollaries. The stable and unstable foliations are codimension one and minimal. By reparameterizing 9 if necessary, the flows (called horocycle flows) generated by the strong stable and strong unstable foliations are also minimal. We therefore have the relations