Mesures invariantes pour les fractions rationnelles géométriquement finies

Tom 160 / 1999

Guillaume Havard Fundamenta Mathematicae 160 (1999), 39-61 DOI: 10.4064/fm-160-1-39-61


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.


  • Guillaume Havard

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