Conformal measures for rational functions revisited

Manfred Denker; R. Mauldin; Z. Nitecki; Mariusz Urbański

Fundamenta Mathematicae (1998)

  • Volume: 157, Issue: 2-3, page 161-173
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Denker, Manfred, et al. "Conformal measures for rational functions revisited." Fundamenta Mathematicae 157.2-3 (1998): 161-173. <http://eudml.org/doc/212283>.

@article{Denker1998,
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.},
author = {Denker, Manfred, Mauldin, R., Nitecki, Z., Urbański, Mariusz},
journal = {Fundamenta Mathematicae},
keywords = {rational function; Riemann sphere; conformal measure; Markov partition; thermodynamic formalism},
language = {eng},
number = {2-3},
pages = {161-173},
title = {Conformal measures for rational functions revisited},
url = {http://eudml.org/doc/212283},
volume = {157},
year = {1998},
}

TY - JOUR
AU - Denker, Manfred
AU - Mauldin, R.
AU - Nitecki, Z.
AU - Urbański, Mariusz
TI - Conformal measures for rational functions revisited
JO - Fundamenta Mathematicae
PY - 1998
VL - 157
IS - 2-3
SP - 161
EP - 173
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.
LA - eng
KW - rational function; Riemann sphere; conformal measure; Markov partition; thermodynamic formalism
UR - http://eudml.org/doc/212283
ER -

References

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