Revisiting Snu spaces with wavelet leaders to detect non concave and non increasing spectra

A multifractal formalism is a formula which is expected to yield the spectrum of singularities of a function from quantities which are numerically computable. The most widespread of these formulas is the so-called thermodynamic mul- tifractal formalism, based on the Frish-Parisi conjecture. It presents two drawbacks: it can hold only for spectra which are concave and it can only yield the increasing part of the spectrum. This first problem can be avoided using Sν spaces. The second one can be taken care using the wavelet leaders method.
In this poster, we present a new multifractal formalism based on a generaliza- tion of the Sν spaces using wavelet leaders. It allows to detect non concave and non increasing spectra. We compare this formalism with the Sν method and the wavelet leaders method. It is based on joint works with F. Bastin, S. Jaffard, T. Kleyntssens and S. Nicolay.