Mesures invariantes pour les fractions rationnelles géométriquement finies
Fundamenta Mathematicae, Tome 160 (1999) no. 1, pp. 39-61
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\frac{p(T)+1}{p(T)}δ>2$. 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{10_4064_fm_160_1_39_61,
author = {Guillaume Havard},
title = {Mesures invariantes pour les fractions rationnelles g\'eom\'etriquement finies},
journal = {Fundamenta Mathematicae},
pages = {39--61},
publisher = {mathdoc},
volume = {160},
number = {1},
year = {1999},
doi = {10.4064/fm-160-1-39-61},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-160-1-39-61/}
}
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Guillaume Havard. Mesures invariantes pour les fractions rationnelles géométriquement finies. Fundamenta Mathematicae, Tome 160 (1999) no. 1, pp. 39-61. doi: 10.4064/fm-160-1-39-61
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