Ben Slimane, M. Multifractal formalism for self-similar functions under the action of nonlinear dynamical systems. (English) Zbl 0928.28002 Constructive Approximation 15, No. 2, 209-240 (1999). Multifractal formalism for self-similar functions associated to contractive similitudes has been established by 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. Reviewer: Yimin Xiao (Salt Lake City) Cited in 14 Documents MSC: 28A80 Fractals 26A30 Singular functions, Cantor functions, functions with other special properties 26A18 Iteration of real functions in one variable 28A78 Hausdorff and packing measures 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 54H20 Topological dynamics (MSC2010) 37B30 Index theory for dynamical systems, Morse-Conley indices Keywords:Hölder exponent; Besov’s “smoothness” index; Hausdorff dimension; spectrum of singularity; wavelet; multifractal formalism; nonlinear self-similar function Citations:Zbl 0876.42021; Zbl 0876.42022 PDFBibTeX XMLCite \textit{M. Ben Slimane}, Constr. Approx. 15, No. 2, 209--240 (1999; Zbl 0928.28002) Full Text: DOI