论文标题
一个新的组合不变性效果化Anosov在3个manifolds上流动
A new combinatorial invariant caracterizing Anosov flows on 3-manifolds
论文作者
论文摘要
在本文中，我们描述了一种新的方法来解决及3个manifolds上的瞬态Anosov分类问题，直到轨道等效性。更具体地说，我们概括了马尔可夫分区的概念，我们介绍了马尔可夫家族在Anosov流的分化平面上的概念。我们表明，任何瞬态的Anosov流都允许许多马尔可夫家族接受，每个家族都可以在规范上与有限的组合对象集合相关联，称为几何类型。我们证明，任何这样的几何类型都完全描述了在有限的周期性轨道上，流向Dehn-Goodman Fried手术的流动。作为先前结果的必然性，我们表明，任何马尔可夫家族都可以与有限的组合对象集合相关联，称为几何类型，带有周期，每种都描述了流向轨道等效性的流动。
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-Fried surgeries on a finite set of periodic orbits of the flow. As a corollary of the previous result, we show that any Markovian family can be canonically associated to a finite collection of combinatorial objects, called geometric types with cycles, each describing the flow up to orbital equivalence.
