Geodesic
Mathematical Analysis/Dynamical Systems
Hausdorff dimension of the multiplicative golden mean shift
[Dimension de Hausdorff du shift de Fibonacci multiplicatif]

Présenté par : Jean-Pierre Kahane

Kenyon, Richard1 ; Peres, Yuval2 ; Solomyak, Boris3
1 Department of Mathematics, Brown University, Box 1917, 151 Thayer Street, Providence, RI 02912, USA
2 Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA
3 Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA
Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 625-628.

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We compute the Hausdorff dimension of the “multiplicative golden mean shift” defined as the set of all reals in [0,1] whose binary expansion (xk) satisfies xkx2k=0 for all k⩾1, and show that it is smaller than the Minkowski dimension.

Nous calculons la dimension de Hausdorff du « shift de Fibonacci multiplicatif », cʼest-à-dire lʼensemble des nombres réels dans [0,1] dont le développement en binaire (xk) satisfait xkx2k=0 pour tout k⩾1. Nous montrons que la dimension de Hausdorff est plus petite que la dimension de Minkowski.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.05.009

Kenyon, Richard 1 ; Peres, Yuval 2 ; Solomyak, Boris 3

1 Department of Mathematics, Brown University, Box 1917, 151 Thayer Street, Providence, RI 02912, USA
2 Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA
3 Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, USA 
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Kenyon, Richard; Peres, Yuval; Solomyak, Boris. Hausdorff dimension of the multiplicative golden mean shift. Comptes Rendus. Mathématique, Tome 349 (2011) no. 11-12, pp. 625-628. doi : 10.1016/j.crma.2011.05.009. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2011.05.009/

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