Badly approximable systems of affine forms, fractals, and Schmidt games

Details Badly approximable systems of affine forms, fractals, and Schmidt games Badly approximable systems of affine forms, fractals, and Schmidt games

2009-12-13

arxiv.org/abs/0912.2445v2

Mathematics

Dynamical Systems

14 pages, typos corrected in the current version

Scientific paper

A badly approximable system of affine forms is determined by a matrix and a vector. We show Kleinbock's conjecture for badly approximable systems of affine forms: for any fixed vector, the set of badly approximable systems of affine forms is winning (in the sense of Schmidt games) even when restricted to a fractal (from a certain large class of fractals). In addition, we consider fixing the matrix instead of the vector where an analog statement holds.

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