November  2009, 24(4): 1129-1145. doi: 10.3934/dcds.2009.24.1129

On the multifractal formalism for Bernoulli products of invertible matrices

1. 

Département de Matématiques, Faculté des Sciences de Monastir, 5000 Monastir, Tunisia, Tunisia

Received  July 2008 Revised  December 2008 Published  May 2009

We study the multifractal formalism for Bernoulli products of invertible matrices. Using the Fourier-Laplace transform, we prove the existence of a Frostman measure and so the validity of multifractal formalism. As an application we give an estimation of the spectrum of singularities of a harmonic function defined on the Sierpiński gasket.
Citation: Imen Bhouri, Houssem Tlili. On the multifractal formalism for Bernoulli products of invertible matrices. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1129-1145. doi: 10.3934/dcds.2009.24.1129
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