Bernd O. Stratmann
Weak Singularity Spectra of the Patterson measure for Geometrically Finite Kleinian Groups with Parabolic Elements
Preprint series: Mathematica Gottingensis

MSC:

30F40 Kleinian groups

Abstract: In this note we determine the weak singularity spectra of
the Patterson measure
for geometrically finite Kleinian
groups with parabolic elements. This
`weak multifractal
analysis' is based on
afurther investigation of the
Hausdorff dimension of the Jarn\'{\i}k limit
sets, which
represent the natural generalisation of the sets of
well-approximable irrational numbers
to the theory of
Kleinian groups.


Keywords: Limit sets of Kleinian groups, Patterson measure, multifractals