论文标题
严格凸hilbert几何形状中的刻薄性和等分
Ergodicity and equidistribution in strictly convex Hilbert geometry
论文作者
论文摘要
在本文中，我们表明，负面弯曲的riemannian几何形状或更一般的CAT（-1）或Rank-One Cat（0）空间的动力学和计数结果的特征，也适用于严格凸出的凸出的投影结构，配备了其Hilbert Metric。 更具体地说，这些结构承认了有限的沙利文措施。关于这一措施，希尔伯特的大地测量流是强烈的混合，轨道和原始的封闭地球学等分等分，使我们能够渐近地枚举这些物体。
In this paper we show that dynamical and counting results characteristic of negatively-curved Riemannian geometry, or more generally CAT(-1) or rank-one CAT(0) spaces, also hold for geometrically-finite strictly convex projective structures equipped with their Hilbert metric. More specifically, such structures admit a finite Sullivan measure; with respect to this measure, the Hilbert geodesic flow is strongly mixing, and orbits and primitive closed geodesics equidistribute, allowing us to asymptotically enumerate these objects.
