| Invariant measures and the set of exceptions to Littlewood's conjecture (2006) | |||||||||
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.. Comment: 48 pages | |||||||||
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