Dynamics of shear homeomorphisms of tori and the Bestvina-Handel algorithm

An Implementation of the Bestvina-Handel Algorithm for Surface Homeomorphisms

Bestvina and Handel have found an effective algorithm that determines whether a given homeomorphism of an orientable, possibly punctured surface is pseudo-Anosov. We present a software package in Java that realizes this algorithm for surfaces with one puncture. Moreover, the package allows the user to define homeomorphisms in terms of Dehn twists, and in the pseudo-Anosov case it generates images of train tracks in the sense of Bestvina-Handel.

Une nouvelle preuve du theoreme de point fixe de Handel

M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that may be extended to the closed disk and that satisfies a linking property of orbits. We give here a new proof of Handel's fixed point theorem, based on Brouwer theory and some plane topology arguments. We will slightly improve the theorem by proving the existence of a simple closed curve of index 1. This index result was known to be true under an additional hypothesis and has been used by different authors (J Franks [NYJM 2 (1996) 1--19, Trans.AMS 34…

关于同伦布劳威尔理论的分层观点

A foliated viewpoint on homotopy Brouwer theory

本文提出一个统一框架，使Le Calvez的分层方法能够恢复并改进Handel理论的经典结果。

端周期伸缩因子的下界

A lower bound on end-periodic stretch factors

本文针对端周期同胚，以其核特征这一拓扑复杂度度量为变量，给出了Handel--Miller伸缩因子的下界，并证明了该下界增长率的精确性。

每一个弱佩罗数都是一个端周期拉伸因子

Every Weak Perron Number is an End-Periodic Stretch Factor

论文构造了一个端周期的homeomorphism，其Handel-Miller拉伸因子等于给定的弱佩罗数，研究了无限型表面的拉伸因子性质。

Spectral rigidity of automorphic orbits in free groups

It is well-known that a point $T\in cv_N$ in the (unprojectivized) Culler-Vogtmann Outer space $cv_N$ is uniquely determined by its \emph{translation length function} $||.||_T:F_N\to\mathbb R$. A subset $S$ of a free group $F_N$ is called \emph{spectrally rigid} if, whenever $T,T'\in cv_N$ are such that $||g||_T=||g||_{T'}$ for every $g\in S$ then $T=T'$ in $cv_N$. By contrast to the similar questions for the Teichmüller space, it is known that for $N\ge 2$ there does not exist a finite spectrally rigid subset of $F_N$. In this paper we prove that for $N\ge 3$ if $H\le Aut(F_N)$ is a subgroup …