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Invariant measures and the set of exceptions to Littlewood’s conjecture

By Manfred Einsiedler, Anatole Katok and Elon Lindenstrauss


Abstract. We classify the measures on SL(k, R) / SL(k, 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. 1

Year: 2010
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