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Gibbs measures on self-affine Sierpiński carpets and their singularity spectrum

Published online by Cambridge University Press:  01 October 2007

JULIEN BARRAL  and
MOUNIR MENSI
JULIEN BARRAL
Affiliation:
INRIA Rocquencourt, 78153 Le Chesnay cedex, France (email: [email protected])
MOUNIR MENSI
Affiliation:
INRIA Rocquencourt, 78153 Le Chesnay cedex, France (email: [email protected]) Département de Mathématiques, Faculté des Sciences de Monastir, Route de l’Environnement, 5000 Monastir, Tunisia (email: [email protected])
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Abstract

We consider a class of Gibbs measures on self-affine Sierpiński carpets and perform the multifractal analysis of its elements. These deterministic measures are Gibbs measures associated with bundle random dynamical systems defined on probability spaces whose geometrical structure plays a central role. A special subclass of these measures is the class of multinomial measures on Sierpiński carpets. Our result improves the already known result concerning the multifractal nature of the elements of this subclass by considerably weakening and in some cases even eliminating a strong separation condition of geometrical nature.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 5 , October 2007 , pp. 1419 - 1443
Copyright
Copyright © Cambridge University Press 2007

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