Transitions de phase dans l'analyse multifractale de mesures auto-similaires

We show that, contrary to the classical quasi-Bernoulli situation, phase transitions, i.e. points where the Lq-Spectrum τ(q) is not differentiable, may appear if the measure satisfies the weak quasi-Bernoulli property. These transitions are always in (−∞,0] and lead to intervals where the multifractal formalism does not hold. To cite this article: B. Testud, C. R. Acad. Sci. Paris, Ser. I 340 (2005).