论文标题
通过Assouad型尺寸和光谱对Sullivan词典的新观点
A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra
论文作者
论文摘要
Sullivan词典在作用于双曲线空间的Kleinian群体与扩展复合平面的理性地图之间提供了美丽的对应关系。关于相关极限集和朱莉娅集的维度理论，存在一个特别直接的对应关系。在最近的工作中，我们为这些分形集合以及它们支持的某些共形度量建立了用于Assouad型尺寸和光谱的公式。这可以在维度的背景下对两个家庭进行更细微的比较。在这篇说明性文章中，我们讨论了这些结果如何在Sullivan词典中提供新的条目，并揭示了两种设置之间的明显差异。
The Sullivan dictionary provides a beautiful correspondence between Kleinian groups acting on hyperbolic space and rational maps of the extended complex plane. An especially direct correspondence exists concerning the dimension theory of the associated limit sets and Julia sets. In recent work we established formulae for the Assouad type dimensions and spectra for these fractal sets and certain conformal measures they support. This allows a rather more nuanced comparison of the two families in the context of dimension. In this expository article we discuss how these results provide new entries in the Sullivan dictionary, as well as revealing striking differences between the two settings.
