标题： 复动力系统中的曼哈顿曲线和乘子谱的渐近相关性 显示英文标题

标题： Manhattan curves in complex dynamics and asymptotic correlation of multiplier spectra

摘要： 曼哈顿曲线对于给定曲面上的一对双曲结构（可能带有尖点）是一个几何对象，它编码了闭测地线长度相对于两种不同双曲度量的增长率。 它已被广泛研究，作为理解曲面上测地线、测地流的热力学形式化以及比较双曲度量的一种方式。 通过Sullivan的词典，在本文中，我们定义并研究了$\mathbb C\mathbb P^1$上一对双曲有理映射的曼哈顿曲线，以及更一般地，$\mathbb{C}\mathbb{P}^k$上全纯自映射的曼哈顿曲线。 我们讨论了乘子谱的几个计数结果，并表明两个全纯自映射的曼哈顿曲线与其乘子谱的相关数有关。 显示英文摘要

摘要： The Manhattan curve for a pair of hyperbolic structures (possibly with cusps) on a given surface is a geometric object that encodes the growth rate of lengths of closed geodesics with respect to the two different hyperbolic metrics. It has been extensively studied as a way to understand geodesics on surfaces, the thermodynamic formalism of the geodesic flows and comparison of hyperbolic metrics. Via Sullivan's dictionary, in this paper, we define and study the Manhattan curve for a pair of hyperbolic rational maps on $\mathbb C\mathbb P^1$, and more generally of holomorphic endomorphisms of $\mathbb{C}\mathbb{P}^k$. We discuss several counting results for the multiplier spectrum and show that the Manhattan curve for two holomorphic endomorphisms is related to the correlation number of their multiplier spectra.