非正曲面半经典测度的熵
Entropy of semiclassical measures for nonpositively curved surfaces
摘要：
研究了非正截面曲率的紧致黎曼曲面的Laplacian特征函数的渐近性质。我们证明了测地流的半经典测度的Kolmogorov-Sinai熵是由Ruelle上界上界的一半从下到上有界的。我们遵循与Anosov案例相同的主要策略（arXiv：0809.0230）。我们关注主要的区别，并请读者参考（arXiv：0809.0230）以了解类似引理的细节。
英文摘要：
We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.
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