On dimensions of conformal repellers.  Randomness and parameter dependency

Hans Henrik Rugh

doi:10.3934/dcds.2012.32.2553

Article Contents

2012, Volume 32, Issue 7: 2553-2564. Doi: 10.3934/dcds.2012.32.2553

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On dimensions of conformal repellers. Randomness and parameter dependency

Hans Henrik Rugh^1,

1.
Department of Mathematics, University of Paris Sud 11, F-91405 Orsay

Received: December 2009

Revised: July 2010

Published: July 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 37C45, 28A78; Secondary: 60D05, 37H15.

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References

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