论文标题
典型瑟斯顿建筑的伪 - anosov地图的拓扑熵
Topological entropy of pseudo-Anosov maps from a typical Thurston's construction
论文作者
论文摘要
在本文中，我们开发了一种方法来提取有关与典型瑟斯顿建筑相关的随机步行信息的信息。我们首先观察到，典型的瑟斯顿建筑需要一组自由的等级2。我们还提供了与瑟斯顿建筑相关的随机步行的光谱定理证明，这些步行与Teichmüller指标有限的第二时刻。达赫玛尼（Dahmani）和霍贝兹（Horbez）对其总体案件进行了评论。最后，在不涉及力矩条件的假设下，我们证明随机行走最终成为伪anosov。 作为应用程序，我们首先讨论了小岛和麦克沙恩对伪anosov单曲霉的映射圆环的双曲线体积的估计。作为另一项应用，我们讨论了瑟斯顿建筑的伸展因素的非稳定估计，以及塞勒姆数字的权力，成为瑟斯顿建筑中伪anosovs的拉伸因素。
In this paper, we develop a way to extract information about a random walk associated with a typical Thurston's construction. We first observe that a typical Thurston's construction entails a free group of rank 2. We also present a proof of the spectral theorem for random walks associated with Thurston's construction that have finite second moment with respect to the Teichmüller metric. Its general case was remarked by Dahmani and Horbez. Finally, under a hypothesis not involving moment conditions, we prove that random walks eventually become pseudo-Anosov. As an application, we first discuss a random analogy of Kojima and McShane's estimation of the hyperbolic volume of a mapping torus with pseudo-Anosov monodromy. As another application, we discuss non-probabilistic estimations of stretch factors from Thurston's construction and the powers for Salem numbers to become the stretch factors of pseudo-Anosovs from Thurston's construction.
