Measures and Dimensions in Conformal Dynamics

  title={Measures and Dimensions in Conformal Dynamics},
  author={Mariusz Urbanski},
This survey collects basic results concerning fractal and ergodic properties of Julia sets of rational functions of the Riemann sphere. Frequently these results are compared with their counterparts in the theory of Kleinian groups, and this enlarges the famous Sullivan dictionary. The topics concerning Hausdorff and packing measures and dimensions are given most attention. Then, conformal measures are constructed and their relations with Hausdorff and packing measures are discussed throughout… CONTINUE READING
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  • D. Ruelle, Thermodynamic formalism, Encyclopedia of Math., Appl.
  • 5, Addison - Wesley, Reading, Mass.,
  • 1978
Highly Influential
4 Excerpts


  • R. Bowen, Equilibrium states, the ergodic theory for Anosov diffeomorphisms. Lect. N Math
  • Springer,
  • 1975
Highly Influential
4 Excerpts

Urbański, Jarnik and Julia; a Diophantine analysis for parabolic rational maps, Math. Scan

  • M.B.O. Stratmann
  • 2002

Zdunik, Hausdorff dimension of harmonic measure for self-conformal

  • A. UZ M. Urbański
  • sets, Adv. Math
  • 2002

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

  • M. Kesseböhme, B. Stratmann
  • Preprint
  • 2001
2 Excerpts

Hausdorff dimension 2 for Julia sets of quadratic polynomials

  • S. Heinemann, B. Stratmann
  • Math. Z
  • 2001

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