Weak mixing for interval exchange transformations and translation flows

• 成果类型: Article
• 署名作者: Avila, Artur; Forni, Giovanni
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.165.637
• 发表日期: 2007
• 页码: 637-664
• 关键词: area-preserving flows; quadratic-differentials; higher-genus; SURFACES; SPACE; MAPS

摘要

We prove that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a typical translation surface of genus g >= 2 (with prescribed singularity types) is weakly mixing.