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ArticleOriginal scientific text

Title

Conformal measures for rational functions revisited

Authors 1, 2, 3, 2

Affiliations

  1. Institut für Math. Stochastik, Lotzestr. 13, 37083 Göttingen, Germany
  2. Department of Mathematics, University of North Texas, Denton, Texas 76203, U.S.A.
  3. Department of Mathematics, Tufts University Medford, Massachusetts 02155, U.S.A.

Abstract

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.

Bibliography

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Fundamenta Mathematicae
1998/157/2-3
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Pages:
161-173
Main language of publication
English
Received
1997-08-28
Accepted
1998-03-15
Published
1998
Exact and natural sciences