The uniqueness of the maximal measure for geodesic flows on symmetric spaces of higher rank
The uniqueness of the maximal measure for geodesic flows on symmetric spaces of higher rank
复制标题
高阶对称空间上测地线流最大测度的唯一性
DOI：
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发表时间：
2005
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通讯作者：
Gerhard Knieper
中科院分区：
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作者：
Gerhard Knieper
本文证明了非正曲率紧致局部对称空间上的测地线流具有唯一不变的极大熵测度。作为一个应用程序的动力学，我们表明，封闭测地线是均匀分布的，就这个措施。此外，我们证明了在具有非正曲率的紧致局部对称空间中，在具有相同总体积的所有共形等价度量中，体积熵是最小的。
In this paper we show that the geodesic flow on a compact locally symmetric space of nonpositive curvature has a unique invariant measure of maximal entropy. As an application to dynamics we show that closed geodesics are uniformly distributed with respect to this measure. Furthermore, we prove that the volume entropy is minimized at a compact locally symmetric space of nonpositive curvature among all conformally equivalent metrics with the same total volume.