DCDS
On the multifractal formalism for Bernoulli products of invertible matrices
Imen Bhouri Houssem Tlili
Discrete & Continuous Dynamical Systems - A 2009, 24(4): 1129-1145 doi: 10.3934/dcds.2009.24.1129
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.
keywords: Singularity spectrum Frostman measure Lyapunov exponent Hausdorff dimension Sierpi\'nski gasket Multifractal formalism Matrices product Hölder exponent.

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