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

Details Invariant measures and the set of exceptions to Littlewood's conjecture Invariant measures and the set of exceptions to Littlewood's conjecture

2006-12-22

arxiv.org/abs/math/0612721v1

Ann. of Math. (2) 164 (2006), no. 2, 513--560

Mathematics

Dynamical Systems

48 pages

Scientific paper

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.

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