Conformal measures for rational functions revisited

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

Conformal measures for rational functions revisited

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

Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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 language	English (US)
Pages (from-to)	161-173
Number of pages	13
Journal	Fundamenta Mathematicae
Volume	157
Issue number	2-3
State	Published - 1998

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Cite this

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title = "Conformal measures for rational functions revisited",

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.",

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T1 - Conformal measures for rational functions revisited

AU - Denker, M.

AU - Mauldin, R. D.

AU - Nitecki, Z.

AU - Urbański, M.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

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JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

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Conformal measures for rational functions revisited

Abstract

All Science Journal Classification (ASJC) codes

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