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Displaying similar documents to “Euler-Seidel matrices. (Matrices d'Euler-Seidel.)”

Mesures invariantes pour les fractions rationnelles géométriquement finies

Guillaume Havard (1999)

Fundamenta Mathematicae

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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 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.