Badly approximable systems of affine forms, fractals, and Schmidt games
Journal für die reine und angewandte Mathematik
(c) Walter de Gruyter Berlin New York 2011
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.
This is the final version of the article. Available from De Gruyter via the DOI in this record.
Vol. 2011, Iss. 660 (Jan 2011)