Stability of mixing and rapid mixing for hyperbolic flows

• 成果类型: Article
• 署名作者: Field, Michael; Melbourne, Ian; Torok, Andrei
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.166.269
• 发表日期: 2007
• 页码: 269-291
• 关键词: theorem; decay; Axiom

摘要

We obtain general results on the stability of mixing and rapid mixing (superpolynomial decay of correlations) for hyperbolic flows. Amongst C-r Axiom A flows, r >= 2, we show that there is a C-2-open, C-r-dense set of flows for which each nontrivial hyperbolic basic set is rapid mixing. This is the first general result on the stability of rapid mixing (or even mixing) for Axiom A flows that holds in a C-r, as opposed to Holder, topology.