A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups

摘要: We elaborate thermodynamic and multifractal formalisms for general classes of potential functions their average growth rates. then apply these to certain geometrically finite Kleinian groups which may have parabolic elements different ranks. show that our revised give access a description the spectrum ‘homological rates’ in terms Hausdorff dimension. Furthermore, we derive necessary sufficient conditions existence ‘thermodynamic phase transitions’.