Conformal measures for rational functions revisited

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

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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.

Original languageEnglish (US)
Pages (from-to)161-173
Number of pages13
JournalFundamenta Mathematicae
Volume157
Issue number2-3
StatePublished - Dec 1 1998

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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    Denker, M., Mauldin, R. D., Nitecki, Z., & Urbański, M. (1998). Conformal measures for rational functions revisited. Fundamenta Mathematicae, 157(2-3), 161-173.