Asian Journal of Mathematics

Volume 9 (2005)

Number 4

Some Exceptional Phenomena in Multifractal Formalism: Part II

Pages: 473 – 488



De-Jun Feng

Ka-Sing Lau

Ka-Sing Lau

Xiang-Yang Wang

Xiang-Yang Wang


In Part I we showed that the $L^q$-spectrum of the 3-fold convolution of the Cantor measure has a non-differentiable point at a $q_0 < 0$ [LW], therefore the standard multifractal formalism does not hold. In this Part II, we prove a modified multifractal formalism for the measure.

Published 1 January 2005