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

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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.
48 pages

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Dynamical Systems, Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/120587

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0612721
 http://arxiv.org/abs/math/0612721
 Ann. of Math. (2) 164 (2006), no. 2, 513--560

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arXiv