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

100%

Bodart O., Zinsmeister M.

Fundamenta Mathematicae

1996

tom 151

nr 2

121-137

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 $P_c(z)=z^2+c$.

Rectifiability in Teichmüller theory

100%

Astala K., Zinsmeister M.

Banach Center Publications

1995

tom 31

nr 1

45-52

Ograniczanie wyników

1 Banach Center Publications

1 Fundamenta Mathematicae

2 Zinsmeister M.

1 Astala K.

1 Bodart O.

1 1996

1 1995

Wyniki wyszukiwania

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

Rectifiability in Teichmüller theory