On the ergodicity of partially hyperbolic systems

• 成果类型: Article
• 署名作者: Burns, Keith; Wilkinson, Amie
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.171.451
• 发表日期: 2010
• 页码: 451-489
• 关键词: stable ergodicity

摘要

Pugh and Shub have conjectured that essential accessibility implies ergodicity for a C-2, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satisfied in particular by all partially hyperbolic systems with 1-dimensional center bundle. We also obtain ergodicity results for C1+delta partially hyperbolic systems.