On the multifractal formalism       for Bernoulli products of invertible matrices

Imen Bhouri; Houssem Tlili

doi:10.3934/dcds.2009.24.1129

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2009, Volume 24, Issue 4: 1129-1145. Doi: 10.3934/dcds.2009.24.1129

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On the multifractal formalism for Bernoulli products of invertible matrices

Imen Bhouri^1, and
Houssem Tlili^1,

1.
Département de Matématiques, Faculté des Sciences de Monastir, 5000 Monastir

Received: June 30, 2008

Revised: November 30, 2008

Published: October 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 28A80, 28A78, 34D08, 37D35; Secondary: 34D20.

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