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

• Autores: Manfred Einsiedler, Elon Lindenstrauss, Anatole Katok
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 164, Nº 2, 2006, págs. 513-560
• Idioma: inglés
• DOI: 10.4007/annals.2006.164.513
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• Resumen

  • 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.