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arXiv · 2203.04931

The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure

Jonathan M. Fraser·Liam Stuart
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Abstract

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.

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Jonathan M. Fraser, Liam Stuart. 2022-03-09. The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure. https://arxiv.org/abs/2203.04931

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