Invariant measures for the horocycle flow on periodic hyperbolic surfaces
Invariant measures for the horocycle flow on periodic hyperbolic surfaces
复制标题
周期性双曲曲面上的半圆环流的不变测度
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
O. Sarig
中科院分区：
文献类型：
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作者：
F. Ledrappier;O. Sarig
我们对紧双曲曲面上无限正盖环环流的遍历不变Radon测度进行了分类。该方法是在这些测度和曲面拉普拉斯函数的正最小特征函数之间建立一个双射。得到两个结果：如果叠变换群G是多项式增长的，则这些测度由G0到其中G0≤G是有限指标的幂零子群的同态分类；如果群呈指数增长，则在测地线流和环流下可能存在不止一个不变的Radon测度。我们也处理有限体积表面的正则复盖。
We classify the ergodic invariant Radon measures for the horocycle flow on geometrically infinite regular covers of compact hyperbolic surfaces. The method is to establish a bijection between these measures and the positive minimal eigenfunctions of the Laplacian of the surface. Two consequences arise: if the group of deck transformations G is of polynomial growth, then these measures are classified by the homomorphisms from G0 to ℝ where G0 ≤ G is a nilpotent subgroup of finite index; if the group is of exponential growth, then there may be more than one Radon measure which is invariant under the geodesic flow and the horocycle flow. We also treat regular covers of finite volume surfaces.