On the ergodicity of partially hyperbolic systems
On the ergodicity of partially hyperbolic systems
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DOI：
10.4007/annals.2010.171.451
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发表时间：
2005-10
影响因子：
4.9
通讯作者：
K. Burns;A. Wilkinson
中科院分区：
文献类型：
--
作者：
K. Burns;A. Wilkinson
Pugh和Shub猜想，本质可及性蕴含着C的遍历性，部分双曲的保体积微分同态。我们在一个温和的中心聚束假设下证明了这一猜想，这一假设特别地被所有具有一维中心丛的部分双曲组所满足。我们还得到了C1Ci部分双曲组的遍历性结果。
Pugh and Shub have conjectured that essential accessibility implies ergodicity for a C , 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 C 1Ci partially hyperbolic systems.