论文标题
凸射表面重新归一化的希尔伯特长度的相关性
Correlation of the renormalized Hilbert length for convex projective surfaces
论文作者
论文摘要
在本文中，我们着重于（真实）凸射击表面的动力学特性。我们的主要定理为两种不同的凸真射射线结构的自由同型类别的数量提供了一个渐近均值公式。该渐近公式中的相关数是根据其曼哈顿曲线的特征。我们表明，在双曲线表面的空间上，相关数并不均匀地远离零，回答了Schwartz和Sharp的问题。相比之下，我们提供了通过立方射线定义的不同序列的示例，相关数的停留大于均匀的严格正常常数。在最后一节中，我们将相关定理扩展到Hitchin表示。
In this paper we focus on dynamical properties of (real) convex projective surfaces. Our main theorem provides an asymptotic formula for the number of free homotopy classes with roughly the same renormalized Hilbert length for two distinct convex real projective structures. The correlation number in this asymptotic formula is characterized in terms of their Manhattan curve. We show that the correlation number is not uniformly bounded away from zero on the space of pairs of hyperbolic surfaces, answering a question of Schwartz and Sharp. In contrast, we provide examples of diverging sequences, defined via cubic rays, along which the correlation number stays larger than a uniform strictly positive constant. In the last section, we extend the correlation theorem to Hitchin representations.
