Anosov flows on Dehn surgeries on the figure-eight knot

一类不具有紧投影阿诺索夫流的双曲3-流形的无限族

An infinite family of hyperbolic 3-manifolds without tight projectively Anosov flows

本文构造了第一个无限族双曲3-流形，它们具有紧接触结构但不具有紧投影阿诺索夫流，具体通过对八字结进行有理手术得到。

通过双接触结构获得新的Anosov流

New Anosov flows via bicontact structures

本文通过构造带有边界的双接触插件，提出了一种新的超几何插件方法，从而产生新的可传递Anosov流。

Small dilatation pseudo-Anosovs and 3-manifolds

The main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms, ranging over all surfaces. More precisely, we consider pseudo-Anosovs F:S to S with |chi(S)| log(lambda(F)) bounded above by some constant, and we prove that, after puncturing the surfaces at the singular points of the stable foliations, the resulting set of mapping tori is finite. Said differently, there is a finite set of fibered hyperbolic 3-manifolds so that all small dilatation pseudo-Anosovs occur as the monodromy of a Dehn filling on one of the 3-manifolds in…

水平Goodman手术与伪Anosov流的几乎等价性

Horizontal Goodman surgery and almost equivalence of pseudo-Anosov flows

本文推广了Goodman手术操作，证明对传递伪Anosov流进行水平Goodman手术可产生几乎等价的流，并得出相关等价与结构稳定性结果。

Diversified homotopic behavior of closed orbits of some R-covered Anosov flows

We produce infinitely many examples of Anosov flows in closed 3-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of the flow. In the other subset every closed orbit is freely homotopic to only one other closed orbit. The examples are obtained by Dehn surgery on geodesic flows. The manifolds are toroidal and have Seifert fibered pieces and atoroidal pieces in their torus decompositions.

Classification and rigidity of totally periodic pseudo-Anosov flows in graph manifolds

In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a finite power of the free homotopy class of a closed orbit of the flow. We show that each such flow is topologically equivalent to one of the model pseudo-Anosov flows which we constructed in a previous article. A model pseudo-Anosov flow is obtained by glueing standard neighborhoods of Birkhoff annuli and perhaps doing Dehn surgery on certain orbits. We als…

Goodman手术与射影Anosov流

Goodman surgery and projectively Anosov flows

本文将Goodman手术推广至射影Anosov流范畴，，证明了任何接触Anosov流均可通过手术构造新流，并在双曲3-流形上生成新例子，同时将双接触手术与经典接触手术关联并推导出紧性结果。

A new combinatorial invariant caracterizing Anosov flows on 3-manifolds

In this paper, we describe a new approach to the problem of classification of transitive Anosov flows on 3-manifolds up to orbital equivalence. More specifically, generalizing the notion of Markov partition, we introduce the notion of Markovian family of rectangles in the bifoliated plane of an Anosov flow. We show that any transitive Anosov flow admits infinitely many Markovian families, each one of which can be canonically associated to a finite collection of combinatorial objects, called geometric types. We prove that any such geometric type describes completely the flow up to Dehn-Goodman-…

利用双接触几何对 Anosov 流进行手术

Surgery on Anosov flows using bi-contact geometry

本文利用双接触几何定义了一类新的 Anosov 流 Dehn 手术，揭示了 Goodman 手术产生 Anosov 流的条件，并证明了沿简单闭测地线进行 Foulon-Hasselblatt Legendrian 手术是生成接触 Anosov 流的充要条件。

复合辛Dehn扭转的动力学

Dynamics of composite symplectic Dehn twists

本文研究复合辛Dehn扭转的非均匀双曲性，证明其具有正拓扑熵和局部稳定/不稳定拉格朗日流形，并给出A²_m构型的辛映射类群分类。

伪 Anosov 流的 Markov 族

Markovian families for pseudo-Anosov flows

本文提出用双叶平面上的 Markov 族、几何类型与循环等有限组合对象，对三维流形上的伪 Anosov 流进行轨道等价分类。

具有唯一几何块且容许任意多个Anosov流的无穷多图流形

Infinitely many graph manifolds with unique geometrical piece that admit arbitrarily many Anosov flows

本文证明存在无穷多仅含一个几何块的图流形，每个可容许任意多个两两不等价的传递Anosov流，其构造方法与此前基于粘合测地流的方式完全不同。