Geodesic
On the dimensions of conformal repellers. Randomness and parameter dependency
Hans Henrik Rugh1
1 Department of Mathematics, University of Cergy-Pontoise, CNRS UMR 8088, F-95000 Cergy-Pontoise, France
Annals of mathematics, Tome 168 (2008) no. 3, pp. 695-748.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Bowen’s formula relates the Hausdorff dimension of a conformal repeller to the zero of a ‘pressure’ function. We present an elementary, self-contained proof to show that Bowen’s formula holds for $C^1$ conformal repellers. We consider time-dependent conformal repellers obtained as invariant subsets for sequences of conformally expanding maps within a suitable class. We show that Bowen’s formula generalizes to such a repeller and that if the sequence is picked at random then the Hausdorff dimension of the repeller almost surely agrees with its upper and lower box dimensions and is given by a natural generalization of Bowen’s formula. For a random uniformly hyperbolic Julia set on the Riemann sphere we show that if the family of maps and the probability law depend realanalytically on parameters then so does its almost sure Hausdorff dimension.
DOI : 10.4007/annals.2008.168.695

Hans Henrik Rugh 1

1 Department of Mathematics, University of Cergy-Pontoise, CNRS UMR 8088, F-95000 Cergy-Pontoise, France 
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Hans Henrik Rugh. On the dimensions of conformal repellers. Randomness and parameter dependency. Annals of mathematics, Tome 168 (2008) no. 3, pp. 695-748. doi : 10.4007/annals.2008.168.695. http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.168.695/

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