Absence of mixing in area-preserving flows on surfaces

• 成果类型: Article
• 署名作者: Ulcigrai, Corinna
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.3.10
• 发表日期: 2011
• 页码: 1743-1778
• 关键词: interval exchange transformations; deviation; SPACE

摘要

We prove that minimal area-preserving flows locally given by a 3smooth Hamiltonian on a closed surface of genus g <= 2 are typically (in the measure-theoretical sense) not mixing. The result is obtained by cons idering special flows over interval exchange transformations under roof functions with symmetric logarithmic singularities and proving absence of mixing for a full measure set of interval exchange transformations.