INFINITE TYPE FLAT SURFACE MODELS OF ERGODIC SYSTEMS

被引：12

作者：

Lindsey, Kathryn ^{[1
]}

Trevino, Rodrigo ^{[2
]}

机构：

[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[2] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 10期

基金：

美国国家科学基金会;

关键词：

Translation surface; renormalization; Teichmuller dynamics; Bratteli diagram; cutting and stacking; odometer; ergodic; dictionary; UNIQUE ERGODICITY; INVARIANT-MEASURES; BRATTELI DIAGRAMS; TRANSFORMATIONS; FLOWS;

D O I：

10.3934/dcds.2016043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat surfaces. We prove a sufficient condition for ergodicity of this flow and apply the condition to several examples. We present specific examples of infinite type flat surfaces on which the translation flow exhibits dynamical phenomena not realizable by translation flows on finite type flat surfaces.

引用

页码：5509 / 5553

页数：45

共 47 条

[1] Exponential chi-squared distributions in infinite ergodic theory [J].