Geodesic
Invariant measures and the set of exceptions to Littlewood’s conjecture
Manfred Einsiedler1 ; Anatole Katok2 ; Elon Lindenstrauss1
1 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States
2 Department of Mathematics, The Pennsylvania State University, State College, PA 16802, United States
Annals of mathematics, Tome 164 (2006) no. 2, pp. 513-560.

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We classify the measures on $SL(k,\mathbb{R}) / SL(k,\mathbb{Z})$ which are invariant and ergodic under the action of the group $A$ of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood’s conjecture has Hausdorff dimension zero.
DOI : 10.4007/annals.2006.164.513

Manfred Einsiedler 1 ; Anatole Katok 2 ; Elon Lindenstrauss 1

1 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States
2 Department of Mathematics, The Pennsylvania State University, State College, PA 16802, United States 
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Manfred Einsiedler; Anatole Katok; Elon Lindenstrauss. Invariant measures and the set of exceptions to Littlewood’s conjecture. Annals of mathematics, Tome 164 (2006) no. 2, pp. 513-560. doi : 10.4007/annals.2006.164.513. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.513/

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