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