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.
@article{bwmeta1.element.bwnjournal-article-fmv157i2p161bwm,
author = {Manfred Denker and R. Mauldin and Z. Nitecki and Mariusz Urba\'nski},
title = {Conformal measures for rational functions revisited},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {161-173},
zbl = {0915.58041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p161bwm}
}
Denker, Manfred; Mauldin, R.; Nitecki, Z.; Urbański, Mariusz. Conformal measures for rational functions revisited. Fundamenta Mathematicae, Tome 158 (1998) pp. 161-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p161bwm/
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