论文标题
Mineyev Flow，Orbital Counting和Poincaré系列的混合，用于强烈双曲线指标
Mixing of the Mineyev flow, orbital counting and Poincaré series for strongly hyperbolic metrics
论文作者
论文摘要
我们为双曲线组强烈双曲线指标类别获得轨道计数结果。为了实现这一目标，我们结合了涉及Mineyev拓扑流和符号动力学的奇妙理论技术。我们的结果适用于与可接受的，有限的支持，对称的随机步行以及Mineyev Hat Metric相关的绿色指标。我们还描述了与这些指标相关的Poincaré系列的分析域，证明了Mineyev拓扑流的混合结果，并获得了成对度量的相关渐近学。
We obtain orbital counting results for the class of strongly hyperbolic metrics on hyperbolic groups. To achieve this we combine ergodic theoretic techniques involving the Mineyev topological flow and symbolic dynamics. Our results apply to the Green metric associated to an admissible, finitely supported, symmetric random walk and to the Mineyev hat metric. We also describe the domain of analyticity for the Poincaré series associated to these metrics, prove mixing results for the Mineyev topological flow and obtain correlation asymptotics for pairs of metrics.
