arXiv:2203.04931 Abstract | arXiv Analytics

arXiv:2203.04931 [math.DS]Abstract References Reviews Resources

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

Published 2022-03-09Version 1

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.

Comments: 31 pages, 11 figures. This paper used to form part of arXiv:2007.15493 which has subsequently been cut into three pieces

Categories: math.DS, math.CA, math.MG

Subjects: 28A80, 37F32

Keywords: kleinian limit sets, assouad spectrum, assouad dimension, geometrically finite kleinian group, subtle geometric information

Related articles: Most relevant | Search more

arXiv:2401.07168 [math.DS] (Published 2024-01-13)

Assouad spectrum of Gatzouras-Lalley carpets

Amlan Banaji, Jonathan M. Fraser, István Kolossváry, Alex Rutar

arXiv:2108.05408 [math.DS] (Published 2021-08-11)

The Poincaré exponent and the dimensions of Kleinian limit sets

Jonathan M. Fraser

arXiv:2203.11247 [math.DS] (Published 2022-03-21)