M.H. Kesseboehmer, B.O. Stratmann
A Multifractal Formalism for Growth Rates and Applications to Geometrically Finite Kleinian Groups
Preprint series: Mathematica Gottingensis
MSC:
28A80 Fractals, See also {58Fxx}
30F40 Kleinian groups, See also {20H10}
ZDM: I90
Abstract: We elaborate thermodynamic and multifractal formalisms for
general classes of potential functions and their average
growth rates. We then apply these formalisms to certain
geometrically finite Kleinian groups which may have parabolic
elements of different ranks. We show that for these groups
our revised formalisms give access to a description of the
spectrum of `homological growth rates' in terms of Hausdorff
dimension. Furthermore, we derive necessary and sufficient
conditions for the existence of `strong phase transitions'.
Keywords: Multifractals; Thermodynamic Formalism; Kleinian Groups