Abstract
AbstractThe Assouad dimension of the limit set of a geometrically finite Kleinian group with parabolics may exceed the Hausdorff and box dimensions. The Assouadspectrumis 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.
Funder
Leverhulme Trust
Engineering and Physical Sciences Research Council
University of St Andrews
Publisher
Springer Science and Business Media LLC
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