Uniqueness of minimal unstable lamination for discretized Anosov flows

同时层叠

Simultaneous Laminations

研究环面三维流形上伪阿诺索夫轨道空间通用圆的层叠$\Lambda^\pm_u$，证明其由轨道空间边界的稳定和不稳定预层叠确定，且对特定作用，存在有限层叠对集合，使相关最小轨道空间通用圆的$(\Lambda^+_u,\Lambda^-_u)$在其中。

离散化Anosov流的全局稳定性

Global stability of discretized Anosov flows

本文研究离散化Anosov流这一部分双曲微分同胚类，证明其等价定义、$C^1$开闭性、动态相干性与斑块膨胀性，并探讨中心丛唯一可积性及不变叶状结构唯一性，推广了相关研究。

$\mathcal{PML}$上缓慢的南北动力学

Slow north-south dynamics on $\mathcal{PML}$

考虑伪Anosov映射类在$\mathcal{PML}(S)$上的作用.这种作用具有南北动力学，因此，在迭代下，叠层以指数方式收敛到稳定叠层。我们研究了这种收敛速度，并给出了伪Anosov映射类的速度为1，指数衰减的字长的家庭的例子。此外，我们证明这种行为是最坏的可能。

Anosov 与部分双曲微分同胚的强叶状结构的极小性

Minimality of Strong Foliations of Anosov and Partially Hyperbolic Diffeomorphisms

本文研究了部分双曲微分同胚扩张不变叶状结构的极小性，引入了在$C^1$扰动下稳健的s-横截性，并证明了在弱扩张条件下强不稳定叶状结构的稳健极小性及其在环面和唯一Gibbs测度上的应用。

Anosov flows on Dehn surgeries on the figure-eight knot

The purpose of this paper is to classify Anosov flows on the 3-manifolds obtained by Dehn surgeries on the figure-eight knot. This set of 3-manifolds is denoted by M(r) (r is a ratioanl number), which contains the first class of hyperbolic 3-manifolds admitting Anosov flows in history, discovered by Goodman. Combining with the classification of Anosov flows on the sol-manifold M(0) due to Plante, we have: 1. if r is an integer, up to topological equivalence, M(r) exactly carries a unique Anosov flow, which is constructed by Goodman by doing a Dehn-Fried-Goodman surgery on a suspension Anosov f…

完备化预层状结构

Completing Prelaminations

本文研究圆周上横向预层状结构对何时可完备化或实现为平面双叶状结构端点，给出统一刻画并涵盖伪 Anosov 流等奇异情形。