Multifractal analysis and the variance of Gibbs measures

The multifractal decomposition of Gibbs measures for a conformaliterated function system is well known. We look at a finer decompositionwhich also takes into account the rate of convergence. Thisis motivated by the work of Olsen in the self-similar case.Our study of this finer decomposition involves investigationof the variance of Gibbs measures. This is a problem of independentinterest.