平曲面
摘要
曲面上几何、拓扑与动力系统的各类问题，以及某些一维动力系统的问题，导致了对象限类型奇点的平度量封闭的曲面的研究。此类平曲面自然地组织成族，这些族同构于全纯一次微分的模空间。通过研究单个平曲面在Teichmuller测地流与线性群作用下的轨道，可以获得关于其几何与动力学的诸多信息。特别地，Teichmuller测地流扮演了时间加速机器（重整化过程）的角色，使得能够研究区间交换变换与曲面叶状结构的渐近行为。这篇长篇综述试图以轻松的方式呈现Teichmuller动力学中一些选定的思想、概念与事实。
引用
@article{arxiv.math/0609392,
title = {Flat Surfaces},
author = {Anton Zorich},
journal= {arXiv preprint arXiv:math/0609392},
year = {2014}
}
备注
(152 pages; 51 figures) Based on the lectures given by the author at the Les Houches School "Number Theory and Physics" in March of 2003 and at the workshop on dynamical systems in ICTP, Trieste, in July 2004. See "Frontiers in Number Theory, Physics and Geometry. Volume 1: On random matrices, zeta functions and dynamical systems'', P.Cartier; B.Julia; P.Moussa; P.Vanhove (Editors), Springer-Verlag (2006) for the entire collection (including, in particular, the complementary lectures of J.-C. Yoccoz). For a short version see the paper "Geodesics on Flat Surfaces", arXiv.math.GT/0609399