Multifractal analysis of weak Gibbs measures and phase transition — application to some Bernoulli convolutions

For a given expanding d-fold covering transformation of the one-dimensional torus, the notion of weak Gibbs measure is defined by a natural generalization of the classical Gibbs property. For these measures, we prove that the singularity spectrum and the L -spectrum form a Legendre transform pair. The main difficulty comes from the possible existence of… CONTINUE READING