| 中心指数约束的部分双曲系统的遍历性 |
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| 引用本文： | 周云华. 中心指数约束的部分双曲系统的遍历性[J]. 数学学报, 2010, 53(1): 51-54 |
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| 作者姓名： | 周云华 |
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| 作者单位： | 重庆大学数理学院; |
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| 基金项目： | 国家自然科学基金资助项目(10671006) |
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| 摘 要： | 对于给定紧光滑黎曼流形M上的一个C~2保体积部分双曲微分同胚f,若对所有不变测度的中心方向的指数都满足中心指数约束条件,则f本质可达蕴含遍历.特别地,若对所有不变测度,中心方向指数都为零,则f本质可达蕴含遍历.这一结果部分回答了Pesin提出的两个公开问题.
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| 关 键 词： | 部分双曲 遍历 Lyapunov指数 |
| 收稿时间： | 2008-09-24 |
| 修稿时间： | 2009-03-17 |
The Ergodicity of Partially Hyperbolic Systems with Center Bunching |
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| Yun Hua ZHOU College of Mathematics , Physics,Congqing Uinversity,Chongqing ,P.R.China. The Ergodicity of Partially Hyperbolic Systems with Center Bunching[J]. Acta Mathematica Sinica, 2010, 53(1): 51-54 |
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| Authors: | Yun Hua ZHOU College of Mathematics Physics Congqing Uinversity Chongqing P.R.China |
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| Affiliation: | College of Mathematics and Physics, Congqing Uinversity, Chongqing 400044, P. R. China |
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| Abstract: | Let M be a smooth compact Riemmannian manifold,f be a C~2 partially hyperbolic diffeomorphism preserving volume.If f is essential accessible and the central exponents satisfy center bunching condition for all invariant measure,then f is ergodic. Especially,if for all invariant measure of f,the central exponents are zero,then essential accessibility implies ergodicity.These results partially answer two open problems. |
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| Keywords: | partially hyperbolic ergodicity Lyapunov exponents |
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