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

M Kessebohmer, Bernd O Stratmann

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

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 'thermodynamic phase transitions'.

Original languageEnglish
Pages (from-to)141-170
Number of pages30
JournalErgodic Theory and Dynamical Systems
Volume24
Issue number1
DOIs
Publication statusPublished - Feb 2004

Keywords

  • PARABOLIC RATIONAL MAPS
  • THERMODYNAMIC FORMALISM
  • PATTERSON MEASURE
  • LIMIT-SETS
  • ELEMENTS
  • POINTS
  • TRANSFORMATIONS
  • APPROXIMATION
  • DIMENSION
  • EXPONENT

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