Multifractal Formalism for Self-Similar Functions Under the Action of Nonlinear Dynamical Systems

Abstract.

We study functions which are self-similar under the action of some nonlinear dynamical systems. We compute the exact pointwise H{ö}lder regularity, then we determine the spectrum of singularities and the Besov ``smoothness'' index, and finally we prove the multifractal formalism. The main tool in our computation is the wavelet analysis.