Jarník and Julia; a Diophantine analysis for parabolic rational maps for Geometrically Finite Kleinian Groups with Parabolic Elements

Authors

  • B. O. Stratmann
  • M. Urbański

DOI:

https://doi.org/10.7146/math.scand.a-14377

Abstract

In this paper we derive a Diophantine analysis for Julia sets of parabolic rational maps. We generalise two theorems of Dirichlet and Jarník in number theory to the theory of iterations of these maps. On the basis of these results, we then derive a "weak multifractal analysis" of the conformal measure naturally associated with a parabolic rational map. The results in this paper contribute to a further development of Sullivan's famous dictionary translating between the theory of Kleinian groups and the theory of rational maps.

Downloads

Published

2002-09-01

How to Cite

Stratmann, B. O., & Urbański, M. (2002). Jarník and Julia; a Diophantine analysis for parabolic rational maps for Geometrically Finite Kleinian Groups with Parabolic Elements. MATHEMATICA SCANDINAVICA, 91(1), 27–54. https://doi.org/10.7146/math.scand.a-14377

Issue

Section

Articles