Badly approximable points on manifolds

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Addressing a problem of Davenport we show that any finite intersection of the sets of weighted badly approximable points on any analytic nondegenerate manifold in has full dimension. This also extends Schmidt's conjecture on badly approximable points to arbitrary dimensions.
Original languageEnglish
Pages (from-to)1199-1240
Number of pages42
JournalInventiones Mathematicae
Issue number3
Early online date5 Mar 2015
Publication statusPublished - 1 Dec 2015

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  • Diophantine approximation
  • Badly approximable points

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