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Comptes Rendus Mathématique
Volume 343, n° 7
pages 447-452 (octobre 2006)
Doi : 10.1016/j.crma.2006.09.002
Received : 1 September 2006 ;  accepted : 5 September 2006
Ensembles à grande intersection et ubiquité
Sets with large intersection and ubiquity
 

Arnaud Durand
Laboratoire dʼanalyse et de mathématiques appliquées, université Paris XII, 61, avenue du Général de Gaulle, 94010 Créteil cedex, France 

Résumé

Nous définissons de nouvelles classes dʼensembles à grande intersection, qui généralisent celles introduites par K. Falconer. Ces classes contiennent les ensembles qui sont définis à partir de systèmes dʼubiquité homogènes et hétérogènes. De tels ensembles jouent un rôle important en approximation diophantienne et en analyse multifractale. Pour citer cet article : A. Durand, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Abstract

We define new classes of sets with large intersection, which generalize those introduced by K. Falconer. These classes contain the sets which are defined using homogeneous and heterogeneous ubiquitous systems. Such sets play an important role in Diophantine approximation and in multifractal analysis. To cite this article: A. Durand, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.


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