论文标题
克莱琳极限集和帕特森·苏利文措施的补充频谱
The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure
论文作者
论文摘要
具有抛物面的几何有限的克莱尼人组的限制集的限制可能会超过Hausdorff和盒子尺寸。 Assouad \ emph {spectrum}是一个连续的参数化纪念族，在盒子和分形集的盒子和Assouad尺寸之间“插值”。它旨在揭示比隔离框和盒子尺寸更微妙的几何信息。我们对几何有限的克莱尼人组的极限集和相关的帕特森·苏利文度量进行了详细分析。我们的分析揭示了几个新的特征，例如盒子或Assouad尺寸未见不同等级的霍伯尔之间的相互作用。
The Assouad dimension of the limit set of a geometrically finite Kleinian group with parabolics may exceed the Hausdorff and box dimensions. The Assouad \emph{spectrum} is a continuously parametrised family of dimensions which `interpolates' between the box and Assouad dimensions of a fractal set. It is designed to reveal more subtle geometric information than the box and Assouad dimensions considered in isolation. We conduct a detailed analysis of the Assouad spectrum of limit sets of geometrically finite Kleinian groups and the associated Patterson-Sullivan measure. Our analysis reveals several novel features, such as interplay between horoballs of different rank not seen by the box or Assouad dimensions.
