论文标题
截面的截面表面
Surfaces of section for geodesic flows of closed surfaces
论文作者
论文摘要
我们证明了有关封闭的可定向riemannian表面的大地测量流的截面表面存在的几个结果。我们构建的$σ$的表面是伯克霍夫部分，这意味着它们与地球流量的每个足够长的轨道段相交，或者至少它们在$ \ partialpo中具有$ \partialς$中的某些双曲机组件，作为限制的轨道集，这些轨道的轨道集的轨道集的地球轨道流量不返回到$σ$。为了证明这些定理，我们提供了一项研究的研究，该构造的简单封闭地球学的封闭式导向riemannian表面可能具有独立的兴趣。我们的论点基于曲线缩短流。
We prove several results concerning the existence of surfaces of section for the geodesic flows of closed orientable Riemannian surfaces. The surfaces of section $Σ$ that we construct are either Birkhoff sections, meaning that they intersect every sufficiently long orbit segment of the geodesic flow, or at least they have some hyperbolic components in $\partialΣ$ as limit sets of the orbits of the geodesic flow that do not return to $Σ$. In order to prove these theorems, we provide a study of configurations of simple closed geodesics of closed orientable Riemannian surfaces, which may have independent interest. Our arguments are based on the curve shortening flow.
