Quelques résultats sur la dimension de Hausdorff des ensembles de Julia des polynômes quadratiques

Olivier Bodart; Michel Zinsmeister

Fundamenta Mathematicae (1996)

  • Volume: 151, Issue: 2, page 121-137
  • ISSN: 0016-2736

Abstract

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This paper deals with the Hausdorff dimension of the Julia set of quadratic polynomials. It is divided in two parts. The first aims to compute good numerical approximations of the dimension for hyperbolic points. For such points, Ruelle’s thermodynamical formalism applies, hence computing the dimension amounts to computing the zero point of a pressure function. It is this pressure function that we approximate by a Monte-Carlo process combined with a shift method that considerably decreases the computational cost. The second part is a continuity result of the dimension on the real axis at the parabolic point 1/4 for P c ( z ) = z 2 + c .

How to cite

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Bodart, Olivier, and Zinsmeister, Michel. "Quelques résultats sur la dimension de Hausdorff des ensembles de Julia des polynômes quadratiques." Fundamenta Mathematicae 151.2 (1996): 121-137. <http://eudml.org/doc/212185>.

@article{Bodart1996,
author = {Bodart, Olivier, Zinsmeister, Michel},
journal = {Fundamenta Mathematicae},
keywords = {Hausdorff dimension; Julia set; thermodynamical formalism; Monte Carlo process},
language = {fre},
number = {2},
pages = {121-137},
title = {Quelques résultats sur la dimension de Hausdorff des ensembles de Julia des polynômes quadratiques},
url = {http://eudml.org/doc/212185},
volume = {151},
year = {1996},
}

TY - JOUR
AU - Bodart, Olivier
AU - Zinsmeister, Michel
TI - Quelques résultats sur la dimension de Hausdorff des ensembles de Julia des polynômes quadratiques
JO - Fundamenta Mathematicae
PY - 1996
VL - 151
IS - 2
SP - 121
EP - 137
LA - fre
KW - Hausdorff dimension; Julia set; thermodynamical formalism; Monte Carlo process
UR - http://eudml.org/doc/212185
ER -

References

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