Multifractal formalism for self-similar functions under the action of nonlinear dynamical systems
Multifractal formalism for self-similar functions associated to contractive similitudes has been established by \textit{S. Jaffard} [SIAM J. Math. Anal. 28, No. 4, 944-970 (1997; Zbl 0876.42021); ibid. 971-998 (1997; Zbl 0876.42022)]. In this paper, self-similar functions associated to some nonlinear contractions are studied. In particular, the author calculates the Hölder exponents \(\alpha(x)\) of such functions at any point \(x\), the spectrum of singularities and the Besov ``smoothness'' index and proves the multifractal formalism.
scientific article; zbMATH DE number 1289871