Invariant measures and the set of exceptions to Littlewood's conjecture

• 成果类型: Article
• 署名作者: Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.164.513
• 发表日期: 2006
• 页码: 513-560
• 关键词: entropy; RIGIDITY; diffeomorphisms; ergodicity; SUBGROUPS; FLOWS

摘要

We classify the measures on SL(k,R)/SL(k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood's conjecture has Hausdorff dimension zero.