Badly approximable systems of affine forms

Details Badly approximable systems of affine forms Badly approximable systems of affine forms

1998-08-12

arxiv.org/abs/math/9808057v2

J. of Number Theory 79 (1999), 83--102.

Mathematics

Number Theory

15 pages

Scientific paper

We prove an inhomogeneous analogue of W. M. Schmidt's (1969) theorem on
Hausdorff dimension of the set of badly approximable systems of linear forms.
The proof is based on ideas and methods from the theory of dynamical systems,
in particular, on abundance of bounded orbits of mixing flows on homogeneous
spaces of Lie groups.

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