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On dimensions of conformal repellers. Randomness and parameter dependency

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  • We consider random conformal repellers. We show how to apply Bowen's formula for the Hausdorff dimension in this context and prove smoothness of the dimension with respect to parameters. The present article is essentially an extract of [11]. Our aim here is to emphasize the ideas and mechanisms behind rather than mathematical rigor.
    Mathematics Subject Classification: Primary: 37C45, 28A78; Secondary: 60D05, 37H15.

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    H. H. Rugh, On the dimensions of conformal repellers. Randomness and parameter dependency, Ann. Math. (2), 168 (2008), 695-748.doi: 10.4007/annals.2008.168.695.

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