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Journal of the London Mathematical Society Advance Access originally published online on August 10, 2007
Journal of the London Mathematical Society 2007 76(1):57-72; doi:10.1112/jlms/jdm023
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© 2007 London Mathematical Society

Multifractal analysis and the variance of Gibbs measures

T. Jordan and M. Pollicott

Department of Mathematics
Warwick University
Coventry CV4 7AL
United Kingdom
mpollic{at}maths.warwick.ac.uk

The multifractal decomposition of Gibbs measures for a conformal iterated function system is well known. We look at a finer decomposition which also takes into account the rate of convergence. This is motivated by the work of Olsen in the self-similar case. Our study of this finer decomposition involves investigation of the variance of Gibbs measures. This is a problem of independent interest.

tjordan{at}maths.warwick.ac.uk

2000 Mathematics Subject Classification 28A80 (primary), 37D35 (secondary).

Received February 27, 2006; published online August 10, 2007.


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