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Measure rigidity and $p$-adic Littlewood-type problems
Journal article   Open access   Peer reviewed

Measure rigidity and $p$-adic Littlewood-type problems

Manfred Einsiedler and Dmitry Kleinbock
Compositio mathematica, Vol.143(3), pp.689-702
05/2007
DOI: https://doi.org/10.1112/S0010437X07002801

Abstract

invariant measures 37A35 (secondary) 37D40 p$-adic 11J04 (primary) Diophantine approximation Littlewood's conjecture 11J83 rigidity higher rank abelian actions
Various $p$-adic versions of Littlewood's conjecture are investigated, generalizing a set-up considered recently by de Mathan and Teulié. In many cases it is shown that the sets of exceptions to these conjectures have Hausdorff dimension zero. The proof follows the measure ridigity approach of Einsiedler, Katok and Lindenstrauss.
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https://doi.org/10.1112/S0010437X07002801View
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