Multifractal formalism for almost all self-affine measures

Abstract

We conduct the multifractal analysis of self-affine measures for "almost all" family of affine maps. Besides partially extending Falconer's formula of $L^q$-spectrum outside the range $1<q\le 2$, the multifractal formalism is also partially verified.

Accepted by Comm. Math. Phys

References in corpus (3)

• Lyapunov spectrum of asymptotically sub-additive potentials
• Equilibrium states of the pressure function for products of matrices
• Local dimensions of measures on self-affine sets