Mesures invariantes pour les fractions rationnelles géométriquement finies

• Autorzy: Guillaume Havard
• Języki publikacji: FR

Abstrakty

EN

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.

Kategorie tematyczne

• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 160
• Numer: 1
• Strony: 39-61

Daty

wydano

1999

otrzymano

1998-04-20

poprawiono

1998-08-05

poprawiono

1999-02-23

Twórcy

autor

Guillaume Havard

• MAPMO-UMR 6628 Université d'Orléans, B.P. 6759, 45067 Orléans Cedex 2, France

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