Let T be a geometrically finite rational map, p(T) its petal number and δ the Hausdorff dimension of its Julia set. We give a construction of the σ-finite and T-invariant measure equivalent to the δ-conformal measure. We prove that this measure is finite if and only if . Under this assumption and if T is parabolic, we prove that the only equilibrium states are convex combinations of the T-invariant probability and δ-masses at parabolic cycles.
@article{bwmeta1.element.bwnjournal-article-fmv160i1p39bwm,
author = {Guillaume Havard},
title = {Mesures invariantes pour les fractions rationnelles g\'eom\'etriquement finies},
journal = {Fundamenta Mathematicae},
volume = {159},
year = {1999},
pages = {39-61},
zbl = {0984.37049},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv160i1p39bwm}
}
Havard, Guillaume. Mesures invariantes pour les fractions rationnelles géométriquement finies. Fundamenta Mathematicae, Tome 159 (1999) pp. 39-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv160i1p39bwm/
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