Pointwise partial hyperbolicity in three‐dimensional nilmanifolds
Pointwise partial hyperbolicity in three‐dimensional nilmanifolds
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DOI：
10.1112/jlms/jdu013
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发表时间：
2013-02
期刊：
影响因子：
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通讯作者：
A. Hammerlindl;R. Potrie
中科院分区：
文献类型：
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作者：
A. Hammerlindl;R. Potrie
我们证明了一个家庭的流形上的所有（点态或绝对）部分双曲系统是动态相干的存在。这个族是具有幂零、非交换基本群的三维流形的集合。我们进一步将这些流形上的部分双曲系统分类到叶共轭。我们还对那些没有吸引或排斥周期性2-torus的3-torus系统进行了分类。这些分类结果使我们能够证明一些动力学结果，包括最大熵和拟吸引子的存在性和唯一性结果。
We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3‐manifolds with nilpotent, non‐abelian fundamental group. We further classify the partially hyperbolic systems on these manifolds up to leaf conjugacy. We also classify those systems on the 3‐torus that do not have an attracting or repelling periodic 2‐torus. These classification results allow us to prove some dynamical consequences, including existence and uniqueness results for measures of maximal entropy and quasi‐attractors.