INFINITE TYPE FLAT SURFACE MODELS OF ERGODIC SYSTEMS

被引:11
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
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
收藏
页码:5509 / 5553
页数:45
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