论文标题
rauzy垫圈及其厄贡特性周围的动力系统
Dynamical systems around the Rauzy gasket and their ergodic properties
论文作者
论文摘要
在80年代开始的开始时，H.Masur和W.Veech开始研究间隔交换转换的通用特性，证明了几乎每种这种转变都是独特的奇特。大约在同一时间，S.Novikov的学校和法国数学家独立地发现了对表面和各个IET的测量叶子类别的非常有趣的现象。例如，这些家庭在这些家庭中的最低差异很高。此语句的精确版本是Novikov的猜想。法国和俄罗斯建筑是非常不同的。然而，在最简单的情况下（三个属的表面具有两个奇异性），最近观察到，这两种叶子具有相同类型的特性。例如，最小参数的空间是相同的，称为rauzy垫圈。但是，这两个系列作品之间的确切联系还不清楚。本文的目的是证明这两种理论都用不同的语言描述了相同的对象。本文提供了两个构造之间的明确词典。
At the beggining of the 80's, H.Masur and W.Veech started the study of generic properties of interval exchange transformations proving that almost every such transformation is uniquely ergodic. About the same time, S.Novikov's school and French mathematicians independently discovered very intriguing phenomena for classes of measured foliations on surfaces and respective IETs. For instance, minimality is exceptional in these families. A precise version of this statement is a conjecture by Novikov. The French and Russian constructions are very different ones. Nevertheless, in the most simple situation (surfaces of genus three with two singularities) it was recently observed that both foliations share the same type of properties. For instance, the space of minimal parameters is the same, called the Rauzy gasket. However, the precise connection between these two series of works was rather unclear. The aim of this paper is to prove that both theories describe in different languages the same objects. This text provides an explicit dictionary between both constructions.
