Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows
Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows
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DOI：
10.4171/jems/534
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发表时间：
2011-10
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影响因子：
--
通讯作者：
A. Avila;M. Viana;A. Wilkinson
中科院分区：
文献类型：
--
作者：
A. Avila;M. Viana;A. Wilkinson
本文研究了具有负曲率的紧致曲面的测地线流的时一映射的保体积扰动。我们表明，如果刘维尔措施有勒贝格解体沿着中心叶理，然后扰动本身是时间一个光滑的保体积流的地图，否则解体必然是原子。
We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.