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Multifractal analysis and the variance of Gibbs measures

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.