Mesures invariantes pour les fractions rationnelles géométriquement finies

Guillaume Havard

Fundamenta Mathematicae (1999)

  • Volume: 160, Issue: 1, page 39-61
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Havard, Guillaume. "Mesures invariantes pour les fractions rationnelles géométriquement finies." Fundamenta Mathematicae 160.1 (1999): 39-61. <http://eudml.org/doc/212380>.

@article{Havard1999,
author = {Havard, Guillaume},
journal = {Fundamenta Mathematicae},
keywords = {Hausdorff dimension; parabolic cycles; Julia set},
language = {fre},
number = {1},
pages = {39-61},
title = {Mesures invariantes pour les fractions rationnelles géométriquement finies},
url = {http://eudml.org/doc/212380},
volume = {160},
year = {1999},
}

TY - JOUR
AU - Havard, Guillaume
TI - Mesures invariantes pour les fractions rationnelles géométriquement finies
JO - Fundamenta Mathematicae
PY - 1999
VL - 160
IS - 1
SP - 39
EP - 61
LA - fre
KW - Hausdorff dimension; parabolic cycles; Julia set
UR - http://eudml.org/doc/212380
ER -

References

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