Badly approximable systems of affine forms, fractals, and Schmidt games
Einsiedler, M; Tseng, J
Date: 16 June 2011
Journal
Journal für die reine und angewandte Mathematik
Publisher
De Gruyter
Publisher DOI
Abstract
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 ...
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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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