Stably Ergodic Dynamical Systems and Partial Hyperbolicity
Stably Ergodic Dynamical Systems and Partial Hyperbolicity
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DOI：
10.1006/jcom.1997.0437
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发表时间：
1997-03
期刊：
影响因子：
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通讯作者：
C. Pugh;M. Shub
中科院分区：
文献类型：
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作者：
C. Pugh;M. Shub
在本文中，我们表明一点双曲性对于保证稳定的遍历性大有帮助，事实上这可能是必要的。我们的主要定理可以解释为，产生混沌行为（即某些双曲性）的相同现象也会导致稳健的统计行为。我们的理论适用的例子包括某些齐次空间上的平移以及恒定负曲率流形的测地流的一次映射。
In this paper we show that a little hyperbolicity goes a long way toward guaranteeing stable ergodicity, and in fact may be necessary for it. Our main theorem may be interpreted as saying that the same phenomenon producing chaotic behavior (i.e., some hyperbolicity) also leads to robust statistical behavior. Examples to which our theory applies include translations on certain homogeneous spaces and the time-one map of the geodesic flow for a manifold of constant negative curvature.