Geodesic
Hausdorff dimension of the set of singular pairs
Yitwah Cheung1
1 Department of Mathematics<br/>San Francisco State University<br/>San Francisco, CA 94132
Annals of mathematics, Tome 173 (2011) no. 1, pp. 127-167.

Voir la notice de l'article provenant de la source Annals of Mathematics website

In this paper we show that the Hausdorff dimension of the set of singular pairs is $\tfrac{4}{3}$. We also show that the action of $\mathrm{diag}(e^t,e^t,e^{-2t})$ on $\mathrm{SL}_3 \mathbb{R}/\mathrm{SL}_3\mathbb{Z}$ admits divergent trajectories that exit to infinity at arbitrarily slow prescribed rates, answering a question of A. N. Starkov. As a by-product of the analysis, we obtain a higher-dimensional generalization of the basic inequalities satisfied by convergents of continued fractions. As an illustration of the technique used to compute Hausdorff dimension, we reprove a result of I. J. Good asserting that the Hausdorff dimension of the set of real numbers with divergent partial quotients is $\tfrac12$.
DOI : 10.4007/annals.2011.173.1.4

Yitwah Cheung 1

1 Department of Mathematics<br/>San Francisco State University<br/>San Francisco, CA 94132 
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Yitwah Cheung. Hausdorff dimension of the set of singular pairs. Annals of mathematics, Tome 173 (2011) no. 1, pp. 127-167. doi : 10.4007/annals.2011.173.1.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.1.4/

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