Conformal measures for rational functions revisited

Volume 157 / 1998

M. Denker, R. D. Mauldin, Z. Nitecki, M. Urbański Fundamenta Mathematicae 157 (1998), 161-173 DOI: 10.4064/fm_1998_157_2-3_1_161_173


We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.


  • M. Denker
  • R. D. Mauldin
  • Z. Nitecki
  • M. Urbański

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